Question

Select the simplification that accurately explains the following statement.

Answer 1

Answer:

The correct option is D.

Step-by-step explanation:

The given expression is

$\sqrt[3]{7}=7^{\frac{1}{3}}$

Take cube both sides.

$(\sqrt[3]{7})^3=(7^{\frac{1}{3}})^3$

Using exponent property: $a^3=a\times a\times a$

$(7^{\frac{1}{3}})^3=7^{\frac{1}{3}}\times 7^{\frac{1}{3}}\times 7^{\frac{1}{3}}$

Using exponent property: $a^ma^n=a^{m+n}$

$(7^{\frac{1}{3}})^3=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}$

$(7^{\frac{1}{3}})^3=7^{\frac{3}{3}}$

$(7^{\frac{1}{3}})^3=7^1$

$(7^{\frac{1}{3}})^3=7$

Therefore option D is correct.

Answer 2

The correct answer is A because when you solve everything in this equation, it comes out to 7=7=7=7=7, so this is correct. Just use your calculator to solve these.