In Exercises 21–38, rewrite each expression with rational exponen...

Question

In Exercises 21–38, rewrite each expression with rational exponents.
____
(⁶√7xy² ) ⁵

Accepted Answer

Welcome back. I am so glad you're here. And we're asked for the following expression, rewrite using rational exponents. Our expression is open parentheses. The 8th rut of 13 PQ Squared, closed parentheses, all cubed and our answer choices are answer choice. A 13 PQ All raised to the 3/4. Answer choice B 13 PQ Squared, I raise to the 1/8 answer choice C 13 PQ Squared, I'll race to the 8/3 and answer choice D 13 PQ Squared all raised to the 3/8. All right, rational exponents. Those are ones with a ratio or with a fraction. And so we need to look at what's inside of the radical here. We've got 13 P Q squared. Everything in the radical has the root of something being taken. And in this case, it's the eighth rut and they are all being raised to an exponent. In this case, they're all being cubed or raised to the third power. So because they all have both of those operations happening to them, we can put the 13 P Q squared inside a parentheses and raise it to a rational exponent. And now it's just a matter of which parts go, where, where does the root go? Where does the exponent go for our fraction exponent? And so you can think of the root as being like the roots of a tree, they go down in the denominator here of our rational exponent. So our denominator is going to be eight. And you can think of the three floating up here, this exponent like being high up in the clouds that's going to go in the numerator of our rational exponent. So we have open parentheses, 13 P Q squared, closed parentheses, all being raised to the 3/8. We look at our answer choices and this matches with answer choice. D well done. We'll catch you on the next one.

In Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵

Key Concepts

Rational Exponents

Properties of Exponents

Simplifying Expressions

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