Question

Question 5 of 6Which values are equivalent to the fraction below? Check all that apply.11.В.A.31 1c.33OF 3-3

Answer 1

The question is given to be:

$\frac{3^5}{3^8}$

Applying the law of indices:

$\frac{a^m}{a^n}=a^{m-n}$

Therefore, we have the expression to be:

$\frac{3^5}{3^8}=3^{5-8}=3^{-3}$

Recall the law of negative exponents:

$a^{-m}=\frac{1}{a^m}$

Therefore, the expression becomes:

$3^{-3}=\frac{1}{3^3}=\frac{1}{3\times3\times3}=\frac{1}{27}$

The expression is also equivalent to:

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

Since:

$(\frac{1}{3})^3=\frac{1^3}{3^3}=\frac{1}{27}$

ANSWER

The correct options are OPTION C, OPTION E, and OPTION F.