Question

Which of the following is a step in simplifying the expression x multiplied by y to the power of 3 over x to the power of negative 4 multiplied by y to the power of 4, the whole to the power of negative 2.?

Answer 1

Once the rules of exponents are understood, you can begin solving more complicated expressions more easily. Recall that when you take a power to a power, you multiply the exponents, (xa)b= xa·b.

What happens when you raise an entire expression inside parentheses to a power? You can use the techniques you already know to simplify this expression.

(2a)4 = (2a)(2a)(2a)(2a) = (2 • 2 • 2 • 2)(a • a • a • a) = (24)(a4) = 16a4

Notice that the exponent is applied to each factor of 2a. So, we can eliminate the middle steps.

(2a)4 = (24)(a4), applying the 4 to each factor, 2 and a.

= 16a4

The product of two or more numbers raised to a power is equal to the product of each number raised to the same power.