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CHALLENGE PROBLEMSSimplify each expression. The variables represent natural numbers.A. $x^{2 m} x^{3 m}$B. $\left(y^{5}\right)^{4}$C. $\frac{m^{8 x}}{m^{4 x}}$D. $\left(2 a^{6 y}\right)^{4}$

a) $x^{5 m}$.$b)\left(y^{5 c}\right)^{4}=y^{20 c}$c) $\left.m^{8 x} / m^{4 x}=m^{8 x-4 x}=m^{4 x} . d\right)\left(2 a^{6 y}\right)^{4}=16 y^{24 y}$

Algebra

Chapter 5

Exponents and Polynomials

Section 1

Rules for Exponents

Polynomials

Campbell University

Oregon State University

University of Michigan - Ann Arbor

Lectures

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Simplify each expression. …

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we don't simplify the given expressions. Consider the first expression given export to him into export reum. We know that the product will for experience states that cape over Liam into a pavilion. Camp it an escape of a young place. Yeah. So, using the product rule, let us keep the base yet on. Let us at the exponents, William Less 3 a.m. One simplifying this. We get expert, right? Yeah. Now consider the second expression Wipe over fine See raised youto power for We know that the bubble for exponents states that the Emporium this train's due to poverty And then it can build a nice April Young. Yeah, So, using the power room, let us multiply the exponents the white over by sea into four On simplifying this we get wiped over empty sea. Now consider the third subdivision Expo Composite Index Do it by the Emperor for its We know that the potion true for exponents states that a podium by a pavilion camp bitterness a poverty Um my Nastya. So giving the common Basie, um, let us subtract the exponents. Toe eight X minus Four decks on. Simplifying this, We get the amber over four days now consider the next solution. Toa cape over six white raised to power for We know that the product room power off product rule for exponents states that if a product ex wife is raised to two poverty in that it can return US Expo 1,000,000,000 into white poverty. So race each factor off the product to go before we get to Boulder. Four and a over six White raised too powerful to the value off before Forrest 16. And we know that the power room for exponents states that if a pro very amiss reinstitute poverty and then it can return us a bubble yum in here. So we get a proper since white into full you are simplifying this Big 16 give over 24 white.

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