15. Answer the following questions regarding the function

Rewrite the radical expression as an expression with a rational exponent. the seventh root of x to the third power

kherson [118]

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power ⇒ answer A

Step-by-step explanation:

Let us explain how to change the radical expression as an expression

with a rational exponent

1. Find the number of the root and make it the denominator of the

fraction exponent

2. Find the power of the term under the radical and make it the

numerator of the fraction exponent

Examples:

$\sqrt{x^{n}}=x^{\frac{n}{2}}$

$\sqrt[3]{x^{n}}=x^{\frac{n}{3}}$

$\sqrt[5]{x^{n}}=x^{\frac{n}{5}}$

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

∵ the radical expression is the seventh root of x to the third power

∵ seventh root = $\sqrt[7]{}$

∵ x to the third power = x³

∴ seventh root of x to the third power = $\sqrt[7]{x^{3}}$

Let us change it to the rational exponent

∵ $\sqrt[m]{x^{n}}=x^{\frac{n}{m}}$

∵ $\sqrt[7]{x^{3}}$

∴ m = 7 and n = 3

∴ $\sqrt[7]{x^{3}}$ = $x^{\frac{3}{7}}$

∵ $x^{\frac{3}{7}}$ is x to the three sevenths power

∴ $\sqrt[7]{x^{3}}$ is x to the three sevenths power

The expression with a rational exponent of the seventh root of x to the third power is x to the three sevenths power

Learn more:

You can learn more about radical equation is brainly.com/question/7153188

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4 0

3 years ago

Read 2 more answers

$280 is what percent of $3500?

professor190 [17]

Divide then multiply by 100:

280 / 3500 = 0.08

0.08 x 100 = 8%

Answer: 8%

6 0

2 years ago

Read 2 more answers

Tapiwa takes 5% more leaves than adam raked. together they raked 697 liters of leaves

Nina [5.8K]

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Define their percentage:
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Adam = 100%
Tapiwa = 100 + 5 = 105%

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Find their total percentage:
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100 + 105 = 205

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Find 1%
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205% = 697 liters
1% = 3.4 liters

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Find 100% (Adam):
----------------------------------
100% = 3.4 x 100
100% = 340 liters

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Find 105% (Tapiwa):
----------------------------------
105% = 3.4 x 105
105% = 357 liters

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Answer: Tapiwa = 357 liters and Adam = 340 liters.
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8 0

3 years ago

You are hiring a limousine. One company charges a $60 reservation fee plus another $15 per hour. A second company charges a $25

anzhelika [568]

Answer:

7 hours

Step-by-step explanation:

Step one:

given data

let the total charges be y and the number of hours be x

Company A charges

$60 reservation fee plus another $15 per hour.

so

y=60+15x----------1

Company B charges

$25 reservation fee plus another $20 per hour

y=25+20x------------2

Step two:

equate the 2 expressions above we have

60+15x=25+20x

collect like terms

60-25=20x-15x

35=5x

divide both sides by 5

x= 35/5

x= 7 hours

5 0

2 years ago

Mikayla wants to buy a dress that is on sale for 25% off. The original price was $84 and sales tax is 5%. What is the total pric

Feliz [49]

Answer:

$67.20

Step-by-step explanation:

84 x .05

4.2

84 x .25

21

84-21

63

63 + 4.2

67.20

5 0

2 years ago