04.05.2023

Which expression is equivalent to the expression 1/2 to the power of 3 A 3x 1/2
B 1/2 + 1/2 + 1/2
C 1/2 x 1/2 x 1/2
D 3 + 1/2

. 0

Step-by-step answer

09.07.2023, solved by verified expert

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Mathematics
Step-by-step answer
P Answered by PhD
Q1. The answer is D. x4

Let's first rewrite the expression:
x⁵y²/xy² = x⁵/x * y²/y²

Using the rule xᵃ/xᵇ = x(ᵃ⁻ᵇ), we can write the expression as following:
x⁵y²/xy² = x⁵/x * y²/y² = x⁵⁻¹ * y²⁻² = x⁴ * y⁰ = x⁴ * 1 = x⁴

Thus, the correct answer is D.

Q2. The answer is A. 5(5^3/2/5)^2

125 in the form of exponent is 5³.
125 = 5³
Now, let's calculate all choices. 
 
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 5(5³/2/5)² = 5 * (5³ * 5/2)²
                      = 5 * (5³⁺¹/2)²
                      = 5 * (5⁴/2)²
                      = 5 * (5⁴)²/(2)²
                      = 5 * 5⁴*²/4
                      = 5 * 5⁸ / 4
                      = 5¹⁺⁸ / 4
                      = 5⁹/4
                      ≠ 5³ ≠ 125

B. (5³/5⁴)⁻³ = (5³⁻⁴)⁻³
                   = (5⁻¹)⁻³
                   = 5⁽⁻¹⁾*⁽⁻³⁾
                   = 5³
                   = 125

C. 5⁻²/5⁻⁵  = 5⁽⁻²⁾⁻⁽⁻⁵) 
                  = 5⁽⁻²⁾⁺⁵
                  = 5³
                  = 125

D. 5(5⁵/5³) = 5 * 5⁵⁻³
                  = 5 * 5²
                  = 5¹⁺²
                  = 5³
                  = 125

Therefore, the only expression that is not equal to 125 is A.

Q3. The answer is 63x5

Let's check all choices
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 6³x 
6³x/6x⁵ = 6³/6 * x/x⁵
             = 6³⁻¹ * x¹⁻⁵
             = 6²x⁻⁴
             = 36x⁻⁴
             ≠ 36

B. 6³x⁵
6³x⁵/6x⁵ = 6³/6 * x⁵/x⁵
              = 6³⁻¹ * x⁵⁻⁵
              = 6² * x⁰
              = 36 * 1
              = 36

C. 6x⁵ 
6x⁵/6x⁵ = 1
             ≠ 36

D. 6⁷x⁵
6⁷x⁵/6x⁵ = 6⁷/6 * x⁵/x⁵
              = 6⁷⁻¹ * x⁵⁻⁵
              = 6⁶ * x⁰
              = 46656 * 1
              ≠ 36

Therefore, the correct choice is B.

Q4. The answer is

We will use the rule: xᵃ/xᵇ = x(ᵃ⁻ᵇ)

5.4 x 10¹²/1.2 x 10³ = 5.4 / 1.2 x 10¹²/10³
                               = 4.5 x 10¹²⁻³
                               = 4.5 x 10⁹

Q5. The answer is B. To subtract powers with the same base, divide the exponents

Some of the rules regarding operations with exponents are:
xᵃ/xᵇ = x(ᵃ⁻ᵇ) - choice A
xᵃ * xᵇ = x(ᵃ⁺ᵇ) - choice C
(xᵃ)ᵇ = xᵃ*ᵇ - choice D

Through the process of elimination, choice B is not true.
Mathematics
Step-by-step answer
P Answered by PhD
Q1. The answer is D. x4

Let's first rewrite the expression:
x⁵y²/xy² = x⁵/x * y²/y²

Using the rule xᵃ/xᵇ = x(ᵃ⁻ᵇ), we can write the expression as following:
x⁵y²/xy² = x⁵/x * y²/y² = x⁵⁻¹ * y²⁻² = x⁴ * y⁰ = x⁴ * 1 = x⁴

Thus, the correct answer is D.

Q2. The answer is A. 5(5^3/2/5)^2

125 in the form of exponent is 5³.
125 = 5³
Now, let's calculate all choices. 
 
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 5(5³/2/5)² = 5 * (5³ * 5/2)²
                      = 5 * (5³⁺¹/2)²
                      = 5 * (5⁴/2)²
                      = 5 * (5⁴)²/(2)²
                      = 5 * 5⁴*²/4
                      = 5 * 5⁸ / 4
                      = 5¹⁺⁸ / 4
                      = 5⁹/4
                      ≠ 5³ ≠ 125

B. (5³/5⁴)⁻³ = (5³⁻⁴)⁻³
                   = (5⁻¹)⁻³
                   = 5⁽⁻¹⁾*⁽⁻³⁾
                   = 5³
                   = 125

C. 5⁻²/5⁻⁵  = 5⁽⁻²⁾⁻⁽⁻⁵) 
                  = 5⁽⁻²⁾⁺⁵
                  = 5³
                  = 125

D. 5(5⁵/5³) = 5 * 5⁵⁻³
                  = 5 * 5²
                  = 5¹⁺²
                  = 5³
                  = 125

Therefore, the only expression that is not equal to 125 is A.

Q3. The answer is 63x5

Let's check all choices
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 6³x 
6³x/6x⁵ = 6³/6 * x/x⁵
             = 6³⁻¹ * x¹⁻⁵
             = 6²x⁻⁴
             = 36x⁻⁴
             ≠ 36

B. 6³x⁵
6³x⁵/6x⁵ = 6³/6 * x⁵/x⁵
              = 6³⁻¹ * x⁵⁻⁵
              = 6² * x⁰
              = 36 * 1
              = 36

C. 6x⁵ 
6x⁵/6x⁵ = 1
             ≠ 36

D. 6⁷x⁵
6⁷x⁵/6x⁵ = 6⁷/6 * x⁵/x⁵
              = 6⁷⁻¹ * x⁵⁻⁵
              = 6⁶ * x⁰
              = 46656 * 1
              ≠ 36

Therefore, the correct choice is B.

Q4. The answer is

We will use the rule: xᵃ/xᵇ = x(ᵃ⁻ᵇ)

5.4 x 10¹²/1.2 x 10³ = 5.4 / 1.2 x 10¹²/10³
                               = 4.5 x 10¹²⁻³
                               = 4.5 x 10⁹

Q5. The answer is B. To subtract powers with the same base, divide the exponents

Some of the rules regarding operations with exponents are:
xᵃ/xᵇ = x(ᵃ⁻ᵇ) - choice A
xᵃ * xᵇ = x(ᵃ⁺ᵇ) - choice C
(xᵃ)ᵇ = xᵃ*ᵇ - choice D

Through the process of elimination, choice B is not true.
Mathematics
Step-by-step answer
P Answered by PhD
Q1. The answer is D. x4

Let's first rewrite the expression:
x⁵y²/xy² = x⁵/x * y²/y²

Using the rule xᵃ/xᵇ = x(ᵃ⁻ᵇ), we can write the expression as following:
x⁵y²/xy² = x⁵/x * y²/y² = x⁵⁻¹ * y²⁻² = x⁴ * y⁰ = x⁴ * 1 = x⁴

Thus, the correct answer is D.

Q2. The answer is A. 5(5^3/2/5)^2

125 in the form of exponent is 5³.
125 = 5³
Now, let's calculate all choices. 
 
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 5(5³/2/5)² = 5 * (5³ * 5/2)²
                      = 5 * (5³⁺¹/2)²
                      = 5 * (5⁴/2)²
                      = 5 * (5⁴)²/(2)²
                      = 5 * 5⁴*²/4
                      = 5 * 5⁸ / 4
                      = 5¹⁺⁸ / 4
                      = 5⁹/4
                      ≠ 5³ ≠ 125

B. (5³/5⁴)⁻³ = (5³⁻⁴)⁻³
                   = (5⁻¹)⁻³
                   = 5⁽⁻¹⁾*⁽⁻³⁾
                   = 5³
                   = 125

C. 5⁻²/5⁻⁵  = 5⁽⁻²⁾⁻⁽⁻⁵) 
                  = 5⁽⁻²⁾⁺⁵
                  = 5³
                  = 125

D. 5(5⁵/5³) = 5 * 5⁵⁻³
                  = 5 * 5²
                  = 5¹⁺²
                  = 5³
                  = 125

Therefore, the only expression that is not equal to 125 is A.

Q3. The answer is 63x5

Let's check all choices
The rules we will use are:
xᵃ * xᵇ = x(ᵃ⁺ᵇ)
xᵃ/xᵇ = x(ᵃ⁻ᵇ)
(xᵃ)ᵇ = xᵃ*ᵇ

A. 6³x 
6³x/6x⁵ = 6³/6 * x/x⁵
             = 6³⁻¹ * x¹⁻⁵
             = 6²x⁻⁴
             = 36x⁻⁴
             ≠ 36

B. 6³x⁵ 
6³x⁵/6x⁵ = 6³/6 * x⁵/x⁵
              = 6³⁻¹ * x⁵⁻⁵
              = 6² * x⁰
              = 36 * 1
              = 36

C. 6x⁵ 
6x⁵/6x⁵ = 1
             ≠ 36

D. 6⁷x⁵
6⁷x⁵/6x⁵ = 6⁷/6 * x⁵/x⁵
              = 6⁷⁻¹ * x⁵⁻⁵
              = 6⁶ * x⁰
              = 46656 * 1
              ≠ 36

Therefore, the correct choice is B.

Q4. The answer is

We will use the rule: xᵃ/xᵇ = x(ᵃ⁻ᵇ)

5.4 x 10¹²/1.2 x 10³ = 5.4 / 1.2 x 10¹²/10³
                               = 4.5 x 10¹²⁻³
                               = 4.5 x 10⁹

Q5. The answer is B. To subtract powers with the same base, divide the exponents

Some of the rules regarding operations with exponents are:
xᵃ/xᵇ = x(ᵃ⁻ᵇ) - choice A
xᵃ * xᵇ = x(ᵃ⁺ᵇ) - choice C
(xᵃ)ᵇ = xᵃ*ᵇ - choice D

Through the process of elimination, choice B is not true.
Mathematics
Step-by-step answer
P Answered by PhD
Question 1

Given \frac{x^5y^2}{xy^2}
Substituting x = 0 and y = 0 gives \frac{(0)^5(0)^2}{(0)(0)^2}= \frac{0^7}{0^3}=0^{7-3}=0^4

Let's check option A
We have x^6y^5 = (0)^6(0)^5 = 0^{11}

Let's check option B
We have x^5y=(0)^5(0)=0^6

Let's check option C
We have x^4y = (0)^4(0) = (0)^{4+1} = 0^5

Let's check option D
We have x^4 = (0)^4 = 0^4

The expression that gives the same power with \frac{x^5y^2}{xy^2} is the option D

Option D
------------------------------------------------------------------------------------------------------------

Question 2

We will check each option to see which one doesn't give the final value 125

Option A
5( \frac{5^ \frac{3}{2} }{5})^2 
5( \frac{5^ \frac{3}{2} }{5})( \frac{5 \frac{3}{2} }{5})
5( \frac{5^{ \frac{3}{2}+ \frac{3}{2} }}{5^{1+1}})
5( \frac{5^ \frac{6}{2} }{5^2} )
5( \frac{5^3}{5^2})
5(5^{3-2})
5(5) = 25

Option B
( \frac{5^3}{5^4})^{-3}
( \frac{5^4}{5^3})^3
(5^{4-3})^3
(5)^3 = 125

Option C
\frac{5^{-2}}{5^{-5}}
\frac{5^5}{5^2}
5^{5-2} = 5^3 = 125

Option D
5( \frac{5^5}{5^3})
5(5^{5-3}) = 5(5^2) = 5(25) = 125

Option A
---------------------------------------------------------------------------------------------------------------

Question 3

Setting out the sum we have \frac{y}{6x^5} =36
y = (36)(6x^5)
y = (6^2)(6)(x^5)
y = 6^3x^5

Option B
------------------------------------------------------------------------------------------------------------

Question 4

Given \frac{5.4*10^{12}}{1.2^10^3}
\frac{5.4}{1.2} * \frac{10^{12}}{10^3}
4.5 * (10^{12-3})
4.5 * 10^9

Option B
-------------------------------------------------------------------------------------------------------------

Question 5

Option A is CORRECT - when you divide two powers with the same base, you'd subtract the power ⇒ 5³ ÷ 5² = 5³⁻² = 5¹
 
Option B is INCORRECT - When two powers with the same base are subtracted from each other, we'd have to work out the value of each base first before subtracting, i.e. 6³ - 6² = 216 - 36 = 180 ⇒ This isn't the same by doing 6^{3/2} which would give an answer of 14.7

Option C is CORRECT - Multiplying two powers with the same base is by adding the power, i.e. 4³ × 4² = 4³⁺² = 4⁵

Option D is CORRECT - Raising a power by a power is the same as multiplying the two powers, i.e. (12²)³ = 12⁽²⁾⁽³⁾ = 12⁶

ANSWER: Option B
Mathematics
Step-by-step answer
P Answered by PhD
Question 1

Given \frac{x^5y^2}{xy^2}
Substituting x = 0 and y = 0 gives \frac{(0)^5(0)^2}{(0)(0)^2}= \frac{0^7}{0^3}=0^{7-3}=0^4

Let's check option A
We have x^6y^5 = (0)^6(0)^5 = 0^{11}

Let's check option B
We have x^5y=(0)^5(0)=0^6

Let's check option C
We have x^4y = (0)^4(0) = (0)^{4+1} = 0^5

Let's check option D
We have x^4 = (0)^4 = 0^4

The expression that gives the same power with \frac{x^5y^2}{xy^2} is the option D

Option D
------------------------------------------------------------------------------------------------------------

Question 2

We will check each option to see which one doesn't give the final value 125

Option A
5( \frac{5^ \frac{3}{2} }{5})^2 
5( \frac{5^ \frac{3}{2} }{5})( \frac{5 \frac{3}{2} }{5})
5( \frac{5^{ \frac{3}{2}+ \frac{3}{2} }}{5^{1+1}})
5( \frac{5^ \frac{6}{2} }{5^2} )
5( \frac{5^3}{5^2})
5(5^{3-2})
5(5) = 25

Option B
( \frac{5^3}{5^4})^{-3}
( \frac{5^4}{5^3})^3
(5^{4-3})^3
(5)^3 = 125

Option C
\frac{5^{-2}}{5^{-5}}
\frac{5^5}{5^2}
5^{5-2} = 5^3 = 125

Option D
5( \frac{5^5}{5^3})
5(5^{5-3}) = 5(5^2) = 5(25) = 125

Option A
---------------------------------------------------------------------------------------------------------------

Question 3

Setting out the sum we have \frac{y}{6x^5} =36
y = (36)(6x^5)
y = (6^2)(6)(x^5)
y = 6^3x^5

Option B
------------------------------------------------------------------------------------------------------------

Question 4

Given \frac{5.4*10^{12}}{1.2^10^3}
\frac{5.4}{1.2} * \frac{10^{12}}{10^3}
4.5 * (10^{12-3})
4.5 * 10^9

Option B
-------------------------------------------------------------------------------------------------------------

Question 5

Option A is CORRECT - when you divide two powers with the same base, you'd subtract the power ⇒ 5³ ÷ 5² = 5³⁻² = 5¹
 
Option B is INCORRECT - When two powers with the same base are subtracted from each other, we'd have to work out the value of each base first before subtracting, i.e. 6³ - 6² = 216 - 36 = 180 ⇒ This isn't the same by doing 6^{3/2} which would give an answer of 14.7

Option C is CORRECT - Multiplying two powers with the same base is by adding the power, i.e. 4³ × 4² = 4³⁺² = 4⁵

Option D is CORRECT - Raising a power by a power is the same as multiplying the two powers, i.e. (12²)³ = 12⁽²⁾⁽³⁾ = 12⁶

ANSWER: Option B
Mathematics
Step-by-step answer
P Answered by PhD

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

Mathematics
Step-by-step answer
P Answered by PhD

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

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