Question

simplify.
$(2b^2a^3)^4$
write your answer without parentheses.

Explanation:

Step1: Apply power of a product rule

According to the power of a product rule \((xy)^n = x^n y^n\), we can apply this to \((2b^{2}a^{3})^{4}\) as follows:
\((2b^{2}a^{3})^{4}=2^{4}\times(b^{2})^{4}\times(a^{3})^{4}\)

Step2: Calculate each term

• Calculate \(2^{4}\): \(2^{4} = 16\)
• Calculate \((b^{2})^{4}\) using the power of a power rule \((x^m)^n=x^{mn}\): \((b^{2})^{4}=b^{2\times4}=b^{8}\)
• Calculate \((a^{3})^{4}\) using the power of a power rule: \((a^{3})^{4}=a^{3\times4}=a^{12}\)

Step3: Multiply the results together

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

Answer:

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