Question

simplify.

$(-7a^{4}b)^{2}$

write your answer without parentheses.

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So, for \((-7a^{4}b)^{2}\), we can apply this rule to each factor: \((-7)^{2}(a^{4})^{2}(b)^{2}\).

Step2: Simplify each factor

• Simplify \((-7)^{2}\): \((-7)^{2}=49\) (since a negative number squared is positive).
• Simplify \((a^{4})^{2}\): Using the power of a power rule \((x^m)^n = x^{mn}\), we get \(a^{4\times2}=a^{8}\).
• Simplify \((b)^{2}\): This is just \(b^{2}\).

Step3: Multiply the simplified factors

Multiply the results from Step 2 together: \(49\times a^{8}\times b^{2}=49a^{8}b^{2}\).

Answer:

\(49a^{8}b^{2}\)