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Use the power of a quotient rule for exponents to simplify each expression.$$\left(\frac{7 g^{4}}{6 h^{3}}\right)^{2}$$

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$\frac{49 g^{8}}{36 h^{6}}$

Algebra

Chapter 5

Exponents and Polynomials

Section 1

Rules for Exponents

Polynomials

Campbell University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

00:50

Use the quotient rule for …

00:16

Use the power rule and the…

01:10

01:16

Use the power of a product…

01:47

Simplify the given express…

00:48

Use the rules of exponents…

00:42

Use the power of a quotien…

00:44

00:49

00:26

Use the properties of expo…

00:43

Use the quotient rule and …

00:45

00:32

Apply the quotient rule fo…

01:04

01:13

Simplify each expression u…

We need to simplify the given expression using the power of potient rule for exponents. The given expression is 7 g power 4 by 6 h cube the whole square. We know that the power of quotient rule for exponents states that, if the expression x by y the whole power, we shall write this as x, power n divided by y corn. So let us raise the numerator as well as the denominator to power 2. So we get 7 g power 4. The whole square, the whole thing divided by 6, h cube the whole square. We know that the power of product rule for exponents states that if the product x y is raised to power, then it can be written as x, corn into y poverino raise each factor of the numerator, as well as the denominator to power 2. We get 7 square and this g power 4 square by 6 square, and this h cube square. We know that the power of the power rule for exponents states that over the whole corin can be written as over m into so here on simplifying 7 square. We get 49 and using this rule we get g power 4 into 2, divided by 6 square, is 36 point and again using the rule power 3 into 2. So we get 49 g power 8 by 36 h, power 6 point. Hence the solution.

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