Write each expression without negative exponents, and evaluate if...

Question

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4

Accepted Answer

Hello everyone. We're going to use the rules of exponents to evaluate the expression -8 to the negative third power. Recall that in algebra. If our base is not grouped with our negative sign it is seen as two separate things. So we read this as negative and then in parentheses eight to the negative third power. So we're gonna keep that negative sign out front of our parentheses until the very end. Next I notice I have a negative exponent. I need to make that a positive before I can evaluate this expression I do that by moving it to the denominator of my fraction. So it was like having an 8/1 and now the eight to the third is in the denominator the three changes to a positive three. The base of eight does not change the base does not change its sign. Only the exponent we put a one on the top of our fraction just as a placeholder. We never want that empty. So now I can evaluate it, I put that negative back out front because we aren't dealing with it yet. One stays one 8 to the 3rd power is 512. So now I can take care of the negative that's on the outside. So if I multiply a negative one into this fraction. It's like saying I have negative one Over 512. So the solution when we evaluate this is negative one over which is answer choice. D have a good day

Write each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4

Key Concepts

Negative Exponents

Simplifying Expressions

Evaluating Expressions

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