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.?

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.

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