In Exercises 73–84, simplify each expression using the quotients-...

Question

In Exercises 73–84, simplify each expression using the quotients-to-powers rule.

(x³/5)²

Accepted Answer

Hey, everyone in this problem, we're asked to simplify the following expression and write the answer with positive exponents. The expression we given is A to the exponent five divided by eight all squared. We're given four answer choices. Option A A to the exponent 10 divided by 64. Option B 64 divided by A to the exponent 10. Option C 64 -A to the exponent 10. And option D 64 a cubed, we're gonna start by rewriting the expression. We were given a to the exponent five divided by eight squared. Now we have a fraction like this and our exponent is applied to that whole fraction that exponent has to apply to both the numerator and the denominator. So we can split this up to make it easier to work with and write it as A to the exponent five squared divided by eight squared. So in the numerator, we have eight to the exponent five squared. How do we deal with an exponent raised to an exponent? Well, we're called the power rule. If we have X to the exponent M to the exponent and we can write this as X to the exponent M multiplied by N. So when we have an exponent raised to another exponent, we can simplify that into one by multiplying those two exponents together applying this to our numerator, we have a to the exponent five to the exponent two, we multiply those exponents together by multiplied by two is equal to 10. So we have a to the exponent 10 in the denominator, we have eight squared, we know that this is equal to 64. And so we get that our simplified expression with positive exponents is a to the exponent 10 divided by 64. The correct answer choice is therefore choice. A thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²

Key Concepts

Quotients-to-Powers Rule

Exponent Rules

Simplifying Expressions

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