Question

Write your answer as a power or as a product of powers. $$ (-3 a)^{5} \cdot(4 a)^{2} $$

Short answer

\(-3888a^7\)

Step-by-step solution

Apply Exponent to Each Factor Inside Parentheses

The first step is to apply the exponents to each factor inside the parentheses. We have \( (-3)^5 \cdot a^5 \cdot (4)^2 \cdot a^2 \). This simplifies into \( -243 a^5 \cdot 16 a^2 \).

Combine Like Terms

As per the multiplication rule of exponents, when we multiply like bases, we add the exponents. Therefore, \(a^5\) multiplied by \(a^2\) is \(a^{5+2}\) or \(a^7\). Also, the numerical factors will be multiplied together to get -3888.

Finalize the Expression

After combining like terms, the expression simplifies to \(-3888a^7\).