Question

which expression is equivalent to $\frac{6^{5}}{3^{5}}$? $\frac{2^{5}}{2}$, $2^{0}$, $\frac{1}{2^{5}}$, $(2^{5})^{1}$

Explanation:

Step1: Rewrite 6 as 2×3

$\frac{6^{5}}{3^{5}}=\frac{(2\times3)^{5}}{3^{5}}$

Step2: Apply power - of - a - product rule $(ab)^n=a^n\times b^n$

$\frac{(2\times3)^{5}}{3^{5}}=\frac{2^{5}\times3^{5}}{3^{5}}$

Step3: Cancel out $3^{5}$

$\frac{2^{5}\times3^{5}}{3^{5}} = 2^{5}$
Now let's check each option:

• Option $\frac{2^{5}}{2}=2^{5 - 1}=2^{4}$
• Option $2^{0}=1$
• Option $\frac{1}{2^{5}}=2^{- 5}$
• Option $(2^{5})^{1}=2^{5}$

Answer:

$(2^{5})^{1}$