07.03.2022

Write the expression in radical form x^4/5

. 4

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Mathematics
Step-by-step answer
P Answered by Master
Q1. The answer is No because the law of exponents.

x³ * x³ * x³ ≠ x³*³*³

One of the laws of exponents: xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾
x³ * x³ * x³ = x⁽³⁺³⁺³⁾ = x⁹

x⁹ ≠ x³*³*³

Q2. The answer is \sqrt{x}

\frac{1}{ x^{ \frac{-3}{6} } } = \frac{1}{ x^{ \frac{-1}{2} } } = \frac{1}{ x^{-\frac{1}{2} } } \\ \\ x^{-a} = \frac{1}{ x^{a} } \\ \\ \frac{1}{ x^{-a} } = x^{a} \\ \\ \frac{1}{ x^{-\frac{1}{2} } } = x^{\frac{1}{2} } \\ \\ x^{\frac{a}{b} }= \sqrt[b]{ x^{a} } \\ \\ x^{\frac{1}{2} } = \sqrt{x} \\ \\ \\ \frac{1}{ x^{ \frac{-3}{6} } }= \sqrt{x}

Q3. The answer is x^{3/4}.

x^{a/b} = \sqrt[b]{ x^{a} } \\ x^{a}* x^{b} = x^{a+b} \\ \\ \\ \sqrt{x} * \sqrt[4]{x} = x^{1/2} *x ^{1/4} = x^{1/2 + 1/4} = x^{2/4+1/4} = x^{3/4}

Q4. The answer is \sqrt[3]{ x^{2} }

\frac{ x^{a} }{ x^{b} }= x^{a-b} \\ \\ x^{a/b} = \sqrt[b]{ x^{a} } \\ \\ \\ \frac{ x^{5/6} }{ x^{1/6} } =x^{5/6-1/6} = x^{4/6} = x^{2/3} = \sqrt[3]{ x^{2} }

Q5. The answer is 1/x^(-1)  = x^(1/3)*x^(1/3)*x^(1/3)

Solve all choices:
a) \sqrt[b]{ x^{a} }= x^{a/b} \\ \\ \sqrt[4]{ x^{3} } = x^{3/4}

b) x^{a} = \frac{1}{x^{-a} } \\  \\   \frac{1}{ x^{-1} } = x^{1}= x

c) \sqrt[b]{ x^{a} }= x^{a/b} \\  \\  x^{a}* x^{b} = x^{a+b}    \\  \\ 10 \sqrt{ x^{5}}* x^{4} * x^{2}  =10* x^{5/2} *x^{4} * x^{2} =10* x^{5/2+4+2} =10 x^{17/2}

d) x^{a}* x^{b} = x^{a+b} \\  \\  x^{1/3} * x^{1/3} *x^{1/3}= x^{1/3+1/3+1/3} = x^{3/3} = x^{1} =x
Mathematics
Step-by-step answer
P Answered by Master

See Below

Step-by-step explanation:

Question 1

If I am reading your question right and you mean (x3•x3•x3) & (x3•3•3)

The expressions are not equivalent to each other because x3.x3.x3 is equal to 27 x^3  & (x3•3•3) is equal to 27x

if the question is(x^3•x^3•x^3) & (x3•3•3) , they are still not equvalent because (x^3•x^3•x^3) is equal to x^9 and  (x3•3•3) is s equal to 27x

Question 2 I think the question is 1/x^(-3/6)

1/x^(-3/6)  = x^(3/6)/1 = x^(3/6) = x^(1/2) =\sqrt[2]{x}

Question 3

\sqrt{x} . 4 \sqrt{x} = (1) (4) (\sqrt{x}.\sqrt{x})= 4 \sqrt{x^{2} }=4x

Question 4

I think this is x^(5/6) / x^(1/6)  In that case it is

\frac{x^{5/6} }{x^{1/6} } = x^{(5/6 - 1/6)} = x^{4/6}=x^{2/3}=\sqrt[3]{x^{2} }

Question 5

1/(x^-1)   is equivalent to  x^1/3* x^1/3* x^1/3

They both simplify to be x

1/(x^-1)  = (1/x)^-1 = x

x^1/3* x^1/3* x^1/3  = x ^(1/3 +1/3 +1/3) = x^1= x

Mathematics
Step-by-step answer
P Answered by Master
Q1. The answer is No because the law of exponents.

x³ * x³ * x³ ≠ x³*³*³

One of the laws of exponents: xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾
x³ * x³ * x³ = x⁽³⁺³⁺³⁾ = x⁹

x⁹ ≠ x³*³*³

Q2. The answer is \sqrt{x}

\frac{1}{ x^{ \frac{-3}{6} } } = \frac{1}{ x^{ \frac{-1}{2} } } = \frac{1}{ x^{-\frac{1}{2} } } \\ \\ x^{-a} = \frac{1}{ x^{a} } \\ \\ \frac{1}{ x^{-a} } = x^{a} \\ \\ \frac{1}{ x^{-\frac{1}{2} } } = x^{\frac{1}{2} } \\ \\ x^{\frac{a}{b} }= \sqrt[b]{ x^{a} } \\ \\ x^{\frac{1}{2} } = \sqrt{x} \\ \\ \\ \frac{1}{ x^{ \frac{-3}{6} } }= \sqrt{x}

Q3. The answer is x^{3/4}.

x^{a/b} = \sqrt[b]{ x^{a} } \\ x^{a}* x^{b} = x^{a+b} \\ \\ \\ \sqrt{x} * \sqrt[4]{x} = x^{1/2} *x ^{1/4} = x^{1/2 + 1/4} = x^{2/4+1/4} = x^{3/4}

Q4. The answer is \sqrt[3]{ x^{2} }

\frac{ x^{a} }{ x^{b} }= x^{a-b} \\ \\ x^{a/b} = \sqrt[b]{ x^{a} } \\ \\ \\ \frac{ x^{5/6} }{ x^{1/6} } =x^{5/6-1/6} = x^{4/6} = x^{2/3} = \sqrt[3]{ x^{2} }

Q5. The answer is 1/x^(-1)  = x^(1/3)*x^(1/3)*x^(1/3)

Solve all choices:
a) \sqrt[b]{ x^{a} }= x^{a/b} \\ \\ \sqrt[4]{ x^{3} } = x^{3/4}

b) x^{a} = \frac{1}{x^{-a} } \\  \\   \frac{1}{ x^{-1} } = x^{1}= x

c) \sqrt[b]{ x^{a} }= x^{a/b} \\  \\  x^{a}* x^{b} = x^{a+b}    \\  \\ 10 \sqrt{ x^{5}}* x^{4} * x^{2}  =10* x^{5/2} *x^{4} * x^{2} =10* x^{5/2+4+2} =10 x^{17/2}

d) x^{a}* x^{b} = x^{a+b} \\  \\  x^{1/3} * x^{1/3} *x^{1/3}= x^{1/3+1/3+1/3} = x^{3/3} = x^{1} =x
Mathematics
Step-by-step answer
P Answered by Master

1) No. 2) \sqrt{x}3)4x 4) x^{\frac{3}{2}} or \sqrt{x^3}5) B and D.

Step-by-step explanation:

Check the pictures below

1) x^{3} *x^{3}*x^{3}=x^{3+3+3}=x^{9}x^(3*3*3)=x^{27}[/tex]

For the first, we must just  repeat the base e sum the exponents

For the second one, we must multiply the exponents.

According to the Exponents Law.

x^{m}*x^{n} =x^{m+n}\\x^{m*n} =x^{mn}

2)

Here we have three combined Exponent laws, namely:

3)

First on multiplying keep the 4 outside the square root,

4) The starting point of it is reminding that in a fraction, whenever we divide two fractions we have to operate the product of the first fraction times the inverse of the second one.

Then we apply the Exponent Law of a divison between same base powers, repeating the base subtracting the exponents, and simplifying it:

x^{\frac{4}{6}}=x^{\frac{3}{2}}

5)

Check below

b and d, are equivalent between themselves since the same quantities of x are displayed. Notice, all we have used. Exponent Laws and Power Properties


Ineed  and explanations with these 5 questions.question 1is the expression x^3*x^3*x^3equivalent to
Ineed  and explanations with these 5 questions.question 1is the expression x^3*x^3*x^3equivalent to
Ineed  and explanations with these 5 questions.question 1is the expression x^3*x^3*x^3equivalent to
Ineed  and explanations with these 5 questions.question 1is the expression x^3*x^3*x^3equivalent to
Ineed  and explanations with these 5 questions.question 1is the expression x^3*x^3*x^3equivalent to
Mathematics
Step-by-step answer
P Answered by PhD
1.

The expression is 3^{3}\sqrt{21} -6^{3}\sqrt{2a}

We need to solve each power: 27\sqrt{21}-216\sqrt{2a}.

The Greatest common factor between 27 and 216 is 27, so we extract that

27(\sqrt{21}- 8\sqrt{2a}), which is the simplest form.

2.

The expression is 3^{\frac{1}{2} } \times 3^{\frac{1}{2} }

Notice that bases are equal, that means we need to sum exponents only to find the simplest form

3^{\frac{1}{2} +\frac{1}{2} }=3^{1}=3

3.

The expression is \sqrt[n]{x^{m} }

Here we transform the root into a fractional exponent.

\sqrt[n]{x^{m} }=x^{\frac{m}{n} }

4.

The expression is

\frac{\sqrt{250x^{16} } }{\sqrt{2x} }

Here we need to express it as the root of a fraction

\sqrt{\frac{250x^{16} }{2x} }

Then, we divide

\sqrt{\frac{250x^{16} }{2x} }=\sqrt{125x^{10-1} } =\sqrt{125x^{9} }

5.

The equation is \sqrt{2x+13}-5=x

First, we move the term 5 to other side, then we elevate the equality to the square power to eliminate the square root. Consequently, we have to solve the square power of the binomial x+5:

(\sqrt{2x+13} )^{2} =(x+5)^{2} \\2x+13=x^{2} +10x+25

Then, we move all terms to one side

x^{2} +10x+25-2x-13=0\\x^{2} +8x+12=0

Now, we have to find to numbers which product is 12 and which sum is 8, those numbers are 6 and 2:

\x^{2} +8x+12=(x+6)(x+2)

The solutions are -6 and -2.

6.

The expression is

3\sqrt[5]{(x+2)^{3} }   +3=27

First, we subtract the equation by 3, then we divide by 3:

3\sqrt[5]{(x+2)^{3} } 3-3 =27-3\\3\sqrt[5]{(x+2)^{3} } =24\\\frac{3\sqrt[5]{(x+2)^{3} } }{3}=\frac{24}{3}\\  \sqrt[5]{(x+2)^{3} } =8

Then, we elevate each side to the fifth power to eliminate the root

(\sqrt[5]{(x+2)^{3} } )^{5} =8^{5} \\(x+2)^{3} =32768

Now, we apply a cubic root to each side

\sqrt[3]{(x+2)^{3}}  =\sqrt[3]{32768} \\x+2=32\\x+2-2=32-2\\ \therefore x=30

Mathematics
Step-by-step answer
P Answered by PhD
1.

The expression is 3^{3}\sqrt{21} -6^{3}\sqrt{2a}

We need to solve each power: 27\sqrt{21}-216\sqrt{2a}.

The Greatest common factor between 27 and 216 is 27, so we extract that

27(\sqrt{21}- 8\sqrt{2a}), which is the simplest form.

2.

The expression is 3^{\frac{1}{2} } \times 3^{\frac{1}{2} }

Notice that bases are equal, that means we need to sum exponents only to find the simplest form

3^{\frac{1}{2} +\frac{1}{2} }=3^{1}=3

3.

The expression is \sqrt[n]{x^{m} }

Here we transform the root into a fractional exponent.

\sqrt[n]{x^{m} }=x^{\frac{m}{n} }

4.

The expression is

\frac{\sqrt{250x^{16} } }{\sqrt{2x} }

Here we need to express it as the root of a fraction

\sqrt{\frac{250x^{16} }{2x} }

Then, we divide

\sqrt{\frac{250x^{16} }{2x} }=\sqrt{125x^{10-1} } =\sqrt{125x^{9} }

5.

The equation is \sqrt{2x+13}-5=x

First, we move the term 5 to other side, then we elevate the equality to the square power to eliminate the square root. Consequently, we have to solve the square power of the binomial x+5:

(\sqrt{2x+13} )^{2} =(x+5)^{2} \\2x+13=x^{2} +10x+25

Then, we move all terms to one side

x^{2} +10x+25-2x-13=0\\x^{2} +8x+12=0

Now, we have to find to numbers which product is 12 and which sum is 8, those numbers are 6 and 2:

\x^{2} +8x+12=(x+6)(x+2)

The solutions are -6 and -2.

6.

The expression is

3\sqrt[5]{(x+2)^{3} }   +3=27

First, we subtract the equation by 3, then we divide by 3:

3\sqrt[5]{(x+2)^{3} } 3-3 =27-3\\3\sqrt[5]{(x+2)^{3} } =24\\\frac{3\sqrt[5]{(x+2)^{3} } }{3}=\frac{24}{3}\\  \sqrt[5]{(x+2)^{3} } =8

Then, we elevate each side to the fifth power to eliminate the root

(\sqrt[5]{(x+2)^{3} } )^{5} =8^{5} \\(x+2)^{3} =32768

Now, we apply a cubic root to each side

\sqrt[3]{(x+2)^{3}}  =\sqrt[3]{32768} \\x+2=32\\x+2-2=32-2\\ \therefore x=30

Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram

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