Question

simplify.$(2w^{6}x^{-4})^{5}$write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

Distribute the exponent 5 to each factor inside the parentheses:
$(2w^6x^{-4})^5 = 2^5 \cdot (w^6)^5 \cdot (x^{-4})^5$

Step2: Calculate each exponent term

Compute the powers:
$2^5 = 32$, $(w^6)^5 = w^{6 \times 5} = w^{30}$, $(x^{-4})^5 = x^{-4 \times 5} = x^{-20}$
Combine them: $32w^{30}x^{-20}$

Step3: Convert negative exponent to positive

Use the rule $a^{-n} = \frac{1}{a^n}$ to rewrite $x^{-20}$:
$32w^{30}x^{-20} = \frac{32w^{30}}{x^{20}}$

Answer:

$\frac{32w^{30}}{x^{20}}$