In Exercises 59–72, simplify each expression using the products-t...

Question

In Exercises 59–72, simplify each expression using the products-to-powers rule.

(4x)³

Accepted Answer

Hey, everyone in this problem, we're asked to use the power rule to work out the given expression. And the expression we're given is three Z all to the exponent five. We have four answer choices. Option A 243 Z to the exponent five. Option B 81, Z to the exponent 15. Option C81 Z to the exponent five and option D 243 Z to the exponent 15, we're gonna start by rewriting what we were given. So in brackets, we have three Z and that is raised to the exponent of five. Now, when we have an exponent applied to something in brackets where we have the two things multiplied together, that exponent applies to both of those terms. So we can write this as three to the exponent five multiplied by Z to the exponent five, 3 to the exponent five. This gives us 243. And then we have Z and in reality, we have an exponent one here inside of our bracket. And that's raised to the exponent five. And we're called the power rule. We have a to the exponent M to the exponent N, we can write this as a to the exponent M multiplied by N. So if we have an exponent raised to an exponent, we can simplify this into a single exponent where the two original exponents are multiplied together. So here we have Z to the exponent one to the exponent five. OK, we multiply the two together one multiplied by five gives us five. And so we get Z to the exponent five. So using the power rule, we worked out the simplified expression and it's equal to 243 Z to the exponent five. This corresponds with answer choice A, that's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³

Key Concepts

Exponents

Products-to-Powers Rule

Simplifying Expressions

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