Answer:
Explanation:
I'll explain step by step how to simplify the expression w^5(w^2)^-4.
Step 1: Simplify the exponent inside the parentheses
The first step is to simplify the exponent inside the parentheses. The exponent of -4 means that we need to take the reciprocal of w^2 to get rid of the negative exponent. Using the reciprocal property of exponents, we can rewrite (w^2)^-4 as 1/(w^2)^4 or 1/w^8.
w^5(w^2)^-4 = w^5 * 1/w^8
Step 2: Combine the terms with the same base
Next, we can simplify the expression by multiplying the two terms with the same base of w. Using the product of powers property of exponents, we can add the exponents of w:
w^5 * 1/w^8 = w^(5-8) = w^(-3)
Step 3: Rewrite the expression in simplified form
The final step is to rewrite the expression in simplified form. We have a negative exponent, so we can rewrite w^-3 as 1/w^3. Therefore, the simplified expression is:
w^5(w^2)^-4 = 1/w^3
I hope this explanation helps!