In Exercises 35–52, write each expression with positive exponents...

Question

In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible.

a⁻⁴b⁷/c⁻³

Accepted Answer

Hey, everyone in this problem, we're asked to simplify the following expression and to write the final answer using positive exponents. The expression for given is A to the exponent negative five multiplied by B to the exponent eight divided by C to the exponent -6. We're given four answer choices. Option A B to the exponent eight multiplied by C to the exponent six divided by A to the exponent five. Option B B to the exponent eight multiplied by A to the exponent six divided by B to the exponent five. Option C A to the exponent eight multiplied by C to the exponent six divided by B to the exponent five. And option DB to the exponent eight divided by B to the exponent six multiplied by A to the exponent five. We're gonna start by rewriting the expression we were given. So we have A to the exponent negative five multiplied by B to the exponent eight divided by C to the exponent negative six. Now are called the rule for dealing with negative exponents. If we have X to the exponent negative N, we can write this as one over X to the exponent N OK. So we put the entire expression, the base and the exponent in the denominator and the bait or the exponent sorry becomes positive. So this gives us a way to deal with this A to the negative five term. Now imagine if negative N was equal to M and we can rewrite this expression as X to the exponent N is equal to one over X to the exponent negative end. These two equations are equivalent. So the first one gives us a way of moving a negative exponent to the denominator. The second one, we can move a negative expo exponent from the denominator up to the numerator. OK. So using both of these, we're gonna be able to simplify our expression. So we have a to the exponent -5. OK. Well, we can write this as one over A to the exponent five. Using our rules for negative exponents. We multiply this by B to the exponent eight and then we divide by C to the exponent -6. Well, one over C to the exponent negative six is equal to C to the exponent six, you just multiply by C to the exponent six. And we can simplify this B to the exponent eight multiplied by C to the exponent six divided by A to the exponent five. That's the simplified expression where we only have positive exponents. If we compare this to our answer choices, we found B to the exponent eight C to the exponent six divided by A to the exponent five is the final answer which corresponds with answer choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³

Key Concepts

Negative Exponents

Simplifying Expressions

Laws of Exponents

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