Question

Which expressions are equivalent to \dfrac{2^5}{6^5}

Answer 1

Answer:

A and B

Step-by-step explanation:

Double negatives reverse each other, therefore making both options negative

Answer 2

We have been given an expression $\frac{2^5}{6^5}$. We are asked to choose the expressions, which are equivalent to our given expression.

Using exponent property $\frac{1}{a^n}=a^{-n}$, we can rewrite our given expression as:

$\frac{2^5}{6^5}=2^5\cdot 6^{-5}$

Upon looking at our given choices, we can see that option D is the correct choice.

Let us simplify our given expression.

$\frac{2^5}{6^5}=\frac{2^5}{(2\cdot 3)^5}$

$\frac{2^5}{6^5}=\frac{2^5}{2^5\cdot 3^5}$

Upon cancelling out $2^5$ from numerator and denominator, we will get:

$\frac{2^5}{6^5}=\frac{1}{3^5}$

Using exponent property $\frac{1}{a^n}=a^{-n}$, we will get:

$\frac{1}{3^5}=3^{-5}$

Therefore, option B is a correct choice as well.