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Simplify each expression. Write all answers with positive exponents. Assume that all variables represent positive real numbers. See Example 5 .$$\left(\frac{p^{-1 / 4} q^{-3 / 2}}{3^{-1} p^{-2} q^{-2 / 3}}\right)^{-2}$$
$\frac{q^{5 / 3}}{9 p^{7 / 2}}$
Algebra
Chapter 10
Roots, Radicals, and Root Functions
Section 2
Rational Exponents
Decimals
Exponents and Polynomials
Equations and Inequalities
Complex Numbers
Missouri State University
University of Michigan - Ann Arbor
Idaho State University
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Okay, so let's start by simplifying our inside terms so we can use our quotient role between our P's and Q's. So that's P to the power of negative 1/4 minus a negative. So that's plus a two and in Q to the power of negative 3/2 minus. And they're gonna say that's plus a +23 all over a 3 to 2 pair of negative one, and that's also part of Native to, and I would simplify what we have. That's piece of part of they could have won over four plus two. So that's a seven over for an acute power of negative 3/2. Close A to over three. So we get a note of 5/6 and in all over 32 part negative one and I'll let's pull in our power of negative, too. So we get P to the power of negative 7/2 on Q Tip our of 5/3, and this is all over three to the power of to Okay, so let's rewrite this with positive expert. So we get Q to the power of 5/3 all over three squared, which is line and NPT part of 7/2
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