Question

Write your answer as a power or as a product of powers. $$ (-2 x y)^{3}\left(-x^{2}\right) $$

Short answer

\(-8x^5y^3\)

Step-by-step solution

Apply the Power of a Product Rule

The first term in our expression is \((-2 x y)^{3}\). We can use the power of a product rule here, which states that \( (a b)^n = a^n b^n \). Re-writing our expression, we get \( -2^3 x^3 y^3 \). After calculating \( -2^3 \), this gives -8, so our simplified expression is now \( -8 x^{3} y^{3} \).

Multiply with Second Term

Then, simply multiply this result with the second term of our expression. The second term is \(-x^2\). So, our new expression becomes \( -8x^{3}y^{3} * -x^{2}\).

Apply the Multiplication Rule for Powers

The multiplication rule states that when multiplying two expressions with the same base, we add the exponents. Here, we have \(x^3\) and \(x^2\) to multiply together. Adding the exponents, we get \( x^{3+2}\) which simplifies to \(x^5\). Our final expression then becomes \( -8x^5y^3 \).