Mathematics: Which of the following expressions is equivalent to that expression? A.(n+4)^5 B.(n+4)^1/5 C.(n+4)^5/3 D.(n+4)^3/5

Which of the following expressions is equivalent

Ответ:

carelee67051

21.01.2022

Mathematics

Option D:

$(n+4)^{\frac{3}{5}}$ is the equivalent expression for $\sqrt[5]{(n+4)^{3}}$ .

Solution:

Given expression:

$\sqrt[5]{(n+4)^{3}}$

To find the equivalent expression for the given expression.

$\sqrt[5]{(n+4)^{3}}$

Using radical rule: $$\sqrt[m]{a}=a^{\frac{1}{m}}$

$$=\left((n+4)^{3}\right)^{\frac{1}{5}}$

Using exponent rule: $$\left(a^{b}\right)^{c}=a^{b c}$

$$=(n+4)^{3 \cdot \frac{1}{5}}$

$$=(n+4)^{\frac{3}{5}}$

$\sqrt[5]{(n+4)^{3}}=(n+4)^{\frac{3}{5}}$

Hence $(n+4)^{\frac{3}{5}}$ is the equivalent expression for $\sqrt[5]{(n+4)^{3}}$ .

Option D is the correct answer.

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Ответ:

zack66828

24.08.2021

Mathematics

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Which of the following expressions is equivalent to that expression?

A.(n+4)^5

B.(n+4)^1/5

C.(n+4)^5/3

D.(n+4)^3/5

Ответ:

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