In Exercises 53–58, simplify each expression using the power rule...

Question

In Exercises 53–58, simplify each expression using the power rule.

(b⁴)⁻³

Accepted Answer

Hello, today we're gonna be using the power rules to simplify the given expression. So what we are given is K raced to the power of eight, race to the power of -7. So the first thing we're gonna want to do is apply the multiplication property for exponents. And that states that if you have a race to the power of M raise to the power of N, you can simplify this by taking the product of both of the exponents and rewrite this as a race to the power of M times N. So if we apply this property to the current expression, we can rewrite this as K race to the power of eight times negative seven and eight times negative seven is going to give us negative 56. So we have K race to the power of negative 56. Now we want to express the expression using positive exponents and we have a property that states that if you have a race of the power of negative M, we can rewrite this as a positive exponent by taking the reciprocal of the exponential value. Or in other words, we can rewrite this as one over a race of the power of positive M. So if we apply this property to the expression, we can go ahead and rewrite this as one over K race, the power of positive 56. And this is going to be the simplified form of the given expression. And with that being said, the answer to this problem is going to be a. So I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 53–58, simplify each expression using the power rule. (b⁴)⁻³

Key Concepts

Power Rule

Negative Exponents

Simplifying Expressions

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