Use the power rules for exponents to simplify the expression. Give your answer in exponential form.

Question

(7a^4*b^8)^2

Answer 1

To simplify the expression \((7a^4b^8)^2\) using the power rules for exponents, we apply the rule \((xy)^n = x^n \cdot y^n\) for each part of the expression.

1. First, distribute the exponent to each factor inside the parentheses: \[ (7a^4b^8)^2 = 7^2 \cdot (a^4)^2 \cdot (b^8)^2 \]

2. Next, calculate each term:

   • \(7^2 = 49\)
   • \((a^4)^2 = a^{4 \cdot 2} = a^8\)
   • \((b^8)^2 = b^{8 \cdot 2} = b^{16}\)

3. Now, combine all the results: \[ 49a^8b^{16} \]

Thus, the simplified expression in exponential form is: \[ \boxed{49a^8b^{16}} \]