Question

Select the simplification that accurately explains the following statement.

Answer 1

Answer:

D

Step-by-step explanation:

1. Use property of exponents:

$(a^b)^c=a^b\cdot ... \cdot a^b\ [\text{ take }c \text{ times } a^b]$

Hence

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

2. Use multiplication property of exponents:

$a^b\cdot a^c=a^{b+c}$

Thus,

$7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}$

3. Since

$\frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1,$

we have that

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