Question

simplify.

$\left(-2a^{2}b^{3}\
ight)^{4}$

write your answer without parentheses.

Explanation:

Step1: Apply power of a product rule

We use the rule \((xy)^n = x^n y^n\) and \((x^m)^n=x^{mn}\) for exponents. So, \((-2a^{2}b^{3})^{4}=(-2)^{4}(a^{2})^{4}(b^{3})^{4}\)

Step2: Calculate each term

First, \((-2)^{4}=16\). Then, \((a^{2})^{4}=a^{2\times4}=a^{8}\) and \((b^{3})^{4}=b^{3\times4}=b^{12}\)

Step3: Multiply the results

Multiply the three terms together: \(16\times a^{8}\times b^{12} = 16a^{8}b^{12}\)

Answer:

\(16a^{8}b^{12}\)