In exponential form, the expression √x is equivalent, №18011302, 16.12.2020 01:03

Mathematics

In exponential form, the expression √x is equivalent to

Step-by-step answer

P Answered by Specialist

x^1/2

Step-by-step explanation:

x^1/2 = x squared, just like

x^1/3 = $\sqrt[3]{x}$

Hope this helps!

StudenGPT

Organisms A and B start out with the same population size. Organism A s population doubles every day. After 5 days, the population stops growing and a virus cuts it in half every day for 3 days. Organism B s population grows at the same rate but is not infected with the virus. After 8 days, how much larger is organism B s population than organism A s population? Answer the questions to find out. 1. By what factor does organism A s population grow in the first five days? Express your answer as an exponential expression. (2 points) 2. The expression

Step-by-step answer

P Answered by Studen AI

Sure, let's go through this problem step by step:

1. In the first five days, Organism A's population doubles each day. Therefore, with each passing day, the rate of growth is multiplied by 2. Since this process happens for 5 days, we can represent the growth as an exponential expression 2^5. This indicates that organism A's population size has grown 32 times its initial size.

2. Over the next 3 days, the population of Organism A decreases by half each day due to a virus. This can be written as (2^(-1))^3, which indicates dividing the population by 2 each day. Simplifying the exponent gives 2^(-3), meaning the population would be 1/8 of what it was at the end of day 5.

3. To get the total change in organism A's population over the 8 days, we combine the increase (2^5) and decrease (2^-3). We do that by multiplying these two together: 2^5 * 2^(-3). Using the rule of multiplying with the same base, we add the exponents: 2^(5-3) = 2^2. So, the population of organism A increases by a factor of 4 times its initial size over the 8-day period.

4. Organism B's population doubles every day for 8 days and isn't affected by the virus. The exponential expression representing this growth is 2^8. This means organism B's population size has grown 256 times its initial size.

5. To find the size difference between organism B's and A's population after 8 days, we divide the population size of organism B by that of organism A. That gives us 2^8 / 2^2. Using the rule of division with the same base, we subtract the exponents: 2^(8-2) = 2^6. As a number not in exponential form, that's 64.

So, Organism B's population is 64 times larger than organism A's after 8 days.

Remember to carefully follow all the advised steps such as double-checking work at each step, careful cancellation of terms in fractions, paying close attention to signs, verifying the final answer and accuracy in factoring expressions.

Mathematics

Nstructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match the expressions with their resultant terms in exponential form. tiles 137 1319 131 13-22 13-14 1315 13-7 pairs resultant terms in exponential form expressions 13-11 × 1316 × 13-3 × 134 ×

Step-by-step answer

P Answered by PhD

51

The complete question in the attached figure

we know that
To multiply powers with the same base, keep the base and adds the exponent
so
Part 1)
$13 ^{-11} *13 ^{16}*13 ^{-3}*13 ^{4}*13 ^{-5} \\ =13 ^{(-11+16-3+4-5)} \\= 13 ^{1}$

the answer part 1) is
$13 ^{1}$

Part 2)
$13 ^{-21} *13 ^{-4}*13 ^{-5}*13 ^{14}*13 ^{-6} \\ =13 ^{(-21-4-5+14-6)} \\= 13 ^{-22}$

the answer part 2) is
$13 ^{-22}$

Part 3)
$13 ^{33} *13 ^{-2}*13 ^{5}*13 ^{-13}*13 ^{-8} \\ =13 ^{(33-2+5-13-8)} \\= 13 ^{15}$

the answer Part 3) is
$13 ^{15}$

Part 4)
$13 ^{0} *13 ^{10}*13 ^{-12}*13 ^{5}*13 ^{4} \\ =13 ^{(0+10-12+5+4)} \\= 13 ^{7}$

the answer part 4) is
$13 ^{7}$

Nstructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

Nstructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

Mathematics

Question 1 In this unit, you learned about common logarithms. Since most calculators can be used to find the values of common logarithms only, it’s desirable to be able to convert logarithms with bases other than 10 to common logarithms. This conversion can be done using the change of base formula. Part A Rewrite the logarithmic equation y = logbm in exponential form. Part B Using a log with base c , take the log of both sides of your answer from part A. Then use the power property and solve for y . Part C The original equation was y=logbm . Use

Step-by-step answer

P Answered by Master

1

Answer and Step-by-step explanation:

Part A: Exponential equation is the "opposite" of logarithmic equation, so:

$y=log_{b}m$

$b^{y}=m$

Part B: Using log with base c:

$log_{c}b^{y}=log_{c}m$

Power property of logarithm states that if the anti-logarithm is elevated at a power, the elevated number can be pulled in front of the logarithm:

$ylog_{c}b=log_{c}m$

Solving for y:

$y=\frac{log_{c}m}{log_{c}b}$

Part C: To facilitate the use of calculators, which only have values for the base-10 log and natural log, we use change of base formula, i.e., transform

$y=log_{b}m$

into

$y=\frac{log_{c}m}{log_{c}b}$

Part D: $(log_{3}z)(log_{z}27)$

Change of base will be:

$log_{3}z=\frac{log_{10}z}{log_{10}3}$

$log_{z}27=\frac{log_{10}27}{log_{10}z}$

Solving:

$(log_{3}z)(log_{z}27)$ = $(\frac{log_{10}z}{log_{10}3})(\frac{log_{10}27}{log_{10}z} )$

$(log_{3}z)(log_{z}27)$ = $\frac{log_{10}27}{log_{10}3}$

$(log_{3}z)(log_{z}27)$ = $\frac{log_{10}3^{3}}{log_{10}3}$

$(log_{3}z)(log_{z}27)$ = $\frac{3log_{10}3}{log_{10}3}$

$(log_{3}z)(log_{z}27)$ = 3

Part E: $log_{7}300$

Using change of base:

$log_{7}300=\frac{log300}{log7}$

$log_{7}300=\frac{2.48}{0.85}$

$log_{7}300$ ≈ 3

Mathematics

(06.01) If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points) Group of answer choices 143 314 14 ⋅ 3. 14 ⋅ 14 ⋅ 14 Flag this Question Question 23 pts (06.01) Simplify the expression 43 + 2(3 − 2). (3 points) Group of answer choices 14 16 66 68 Flag this Question Question 33 pts (06.04) What is the value of 5 + 3x when x = 4? (3 points) Group of answer choices 12 17 32 86 Flag this Question Question 410 pts (06.02) Match the verbal expression

Step-by-step answer

P Answered by Specialist

----------------------------------------------------------------------------------------------------------------

-1 and 1/3

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Step-by-step explanation:

----------------------------------------------------------------------------------------------------------------

This is for people with the question;

In the following algebraic expression, determine the coefficients.

-x-12+3/y

---------------------------------------------------------------------------------------------------------------

Also Theres Proof ↓ [all the Way Down - Screenshot]

----------------------------------------------------------------------------------------------------------------

Message~

Hope

you

have

an

✧・ﾟ: *✧・ﾟ:* Amazing*:・ﾟ✧*:・ﾟ✧

Day~

( ˙ ˘ ˙)βෆ

----------------------------------------------------------------------------------------------------------------

(06.01)

If the side lengths of a cube are 14 feet, what is the correct way to write the expression

Mathematics

Nstructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match the expressions with their resultant terms in exponential form. tiles 137 1319 131 13-22 13-14 1315 13-7 pairs resultant terms in exponential form expressions 13-11 × 1316 × 13-3 × 134 ×

Step-by-step answer

P Answered by PhD

51

The complete question in the attached figure

we know that
To multiply powers with the same base, keep the base and adds the exponent
so
Part 1)
$13 ^{-11} *13 ^{16}*13 ^{-3}*13 ^{4}*13 ^{-5} \\ =13 ^{(-11+16-3+4-5)} \\= 13 ^{1}$

the answer part 1) is
$13 ^{1}$

Part 2)
$13 ^{-21} *13 ^{-4}*13 ^{-5}*13 ^{14}*13 ^{-6} \\ =13 ^{(-21-4-5+14-6)} \\= 13 ^{-22}$

the answer part 2) is
$13 ^{-22}$

Part 3)
$13 ^{33} *13 ^{-2}*13 ^{5}*13 ^{-13}*13 ^{-8} \\ =13 ^{(33-2+5-13-8)} \\= 13 ^{15}$

the answer Part 3) is
$13 ^{15}$

Part 4)
$13 ^{0} *13 ^{10}*13 ^{-12}*13 ^{5}*13 ^{4} \\ =13 ^{(0+10-12+5+4)} \\= 13 ^{7}$

the answer part 4) is
$13 ^{7}$

Nstructions: drag the tiles to the correct boxes to complete the pairs. not all tiles will be used.

Mathematics

Write the expression n-4 using a positive exponent. Leave answer in EXPONENTIAL NOTATION OR EXPONENTIAL FORM. PLEASE HELP ME I DONT HAVE MUCH TIME

Step-by-step answer

P Answered by PhD

1

1/ n^4

Step-by-step explanation:

n^-4

We know that a negative exponent in the numerator moves it to the denomintor

a^-b = 1/a^b

n^-4 = 1/ n^4

Mathematics

(06.01) If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form? (2 points) Group of answer choices 143 314 14 ⋅ 3. 14 ⋅ 14 ⋅ 14 Flag this Question Question 23 pts (06.01) Simplify the expression 43 + 2(3 − 2). (3 points) Group of answer choices 14 16 66 68 Flag this Question Question 33 pts (06.04) What is the value of 5 + 3x when x = 4? (3 points) Group of answer choices 12 17 32 86 Flag this Question Question 410 pts (06.02) Match the verbal expression

Step-by-step answer

P Answered by Master

----------------------------------------------------------------------------------------------------------------

-1 and 1/3

----------------------------------------------------------------------------------------------------------------

Step-by-step explanation:

----------------------------------------------------------------------------------------------------------------

This is for people with the question;

In the following algebraic expression, determine the coefficients.

-x-12+3/y

---------------------------------------------------------------------------------------------------------------

Also Theres Proof ↓ [all the Way Down - Screenshot]

----------------------------------------------------------------------------------------------------------------

Message~

Hope

you

have

an

✧・ﾟ: *✧・ﾟ:* Amazing*:・ﾟ✧*:・ﾟ✧

Day~

( ˙ ˘ ˙)βෆ

----------------------------------------------------------------------------------------------------------------

Mathematics

Write the following expression in radical form (8x)1/2= √ Write the following expression in exponential form. √19 =

Step-by-step answer

P Answered by PhD

1

See below

Step-by-step explanation:

Write the following expression in radical form

(8x)¹/² = $\sqrt{8x}$

Write the following expression in exponential form.

$\sqrt{19}$ = 19¹/²

Mathematics

Complete the work to simplify the expression (–2d5)4. 1. express 4 factors of –2d5: (–2d5)(–2d5)(–2d5)(–2d5) 2. expand the expression: –2 ∙ –2 ∙ –2 ∙ –2 ∙ d5∙ d5∙ d5∙ d5 3. simplify to the exponential form: (–2)4∙ (d5)4 4. evaluate the base 2 power: 16 ∙ (d5)4 5. apply the power of a power: 16dx what is the value of x in the simplified power?

Step-by-step answer

P Answered by PhD

81

The value of x is 20.

Step-by-step explanation:

since on expanding the expression (-2d^5)^4 we are given the following steps.

we just need to find the value of 'x'.

step 1: Express 4 factors of (-2d^5)^4 as $(-2d^5)\times(-2d^5)\times(-2d^5)\times(-2d^5)$

step 2: Expand the expression: –2 ×–2 ×–2 ×–2×d^5×d^5×d^5×d^5

step 3: Simplify to the exponential form: (–2)^4∙ (d^5)^4

step 4: Evaluate the base 2 power: 16 ∙ (d^5)^4 ( as -2×-2×-2×-2=16)

step 5: Apply the power of a power: 16d^20 ( As $(a^b)^c=(a)^{bc}$

Hence the value of x is: 20.

In exponential form, the expression √x is equivalent to

Step-by-step answer

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