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 $(ab)^n=a^n b^n$

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

Step3: Cancel out $3^{5}$ in the numerator and denominator

$\frac{2^{5}\times3^{5}}{3^{5}} = 2^{5}=(2^{5})^{1}$

Answer:

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