Question

simplify the expression: $\frac{2^{8}z^{10}}{2^{6}z^{3}}$options:1. $\frac{2^{14}}{z^{7}}$2. $2^{14}z^{13}$3. $2^{2}z^{7}$4. $\frac{2^{2}}{z^{7}}$

Explanation:

Step1: Simplify the base-2 terms

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$\frac{2^8}{2^6}=2^{8-6}=2^2$

Step2: Simplify the z terms

Use exponent rule $\frac{x^a}{x^b}=x^{a-b}$:
$\frac{z^{10}}{z^3}=z^{10-3}=z^7$

Step3: Combine the simplified terms

Multiply the results from Step1 and Step2:
$2^2 \times z^7 = 2^2 z^7$

Answer:

$2^2 z^7$ (matches the third option: $2^2 z^7$)