Question

write the expression \\(\frac{(2^3)^5}{2^6}\\) as a single power of 2. now write the expression as a single power. \\(\frac{(2^3)^5}{2^6} = \frac{2^{15}}{2^6}\\) \\(= ?\\) options: \\(2^4\\), \\(2^9\\), \\(2^{13}\\), \\(2^{21}\\)

Explanation:

Step1: Simplify numerator via exponent rule

$(2^3)^5 = 2^{3 \times 5} = 2^{15}$

Step2: Divide powers with same base

$\frac{2^{15}}{2^6} = 2^{15-6}$

Step3: Calculate the exponent

$2^{15-6} = 2^9$

Answer:

$2^9$ (Option: $2^9$)