Question

Simplify. $$ \left(-w^{4}\right)^{3} $$

Short answer

The simplified form of \( \left(-w^{4}\right)^{3} \) is \( -w^{12} \)

Step-by-step solution

Identify the base and the exponent inside the parentheses

Here, the base is -w, and the exponent is 4. Inside the parentheses, it is raised to the power of 4 giving \( -w^{4} \)

Apply the power of a power rule

According to the power of a power rule, the overall power is the product of the powers. The power outside the parenthesis is 3, therefore the equation becomes \( (-w^{4*3}) \)

Calculate the new exponent amount

Multiply the exponents 4 and 3 to obtain the new exponent, giving \( -w^{12} \)