Exercise 111 Page 364

a To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression and the denominator is the index.

a^()1 n=sqrt(a) and a^() m n=sqrt(a^m) Let's simplify the expression!

8^(13)

PowToRootD

a^(1n)=sqrt(a)

sqrt(8)

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Calculate root

SplitIntoFactors

Split into factors

sqrt(2 * 2 * 2)

WritePow

Write as a power

sqrt(2^3)

RootPowToNumber

sqrt(a^3)=a

b To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression and the denominator is the index.

a^()1 n=sqrt(a) and a^() m n=sqrt(a^m) Let's simplify the expression!

32^(25)

MoveNumRight

a/b=1/b* a

32^(15 * 2)

ProdInExponent

a^(m* n)=(a^m)^n

(32^(15))^2

PowToRootD

a^(1n)=sqrt(a)

(sqrt(32))^2

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Calculate root

SplitIntoFactors

Split into factors

(sqrt(2 * 2 * 2 * 2*2))^2

WritePow

Write as a power

(sqrt(2^5))^2

RootPowToNumber

sqrt(a^5)=a

2^2

CalcPow

Calculate power

c To simplify the given expression, remember that the numerator of a rational exponent is the exponent of the expression and the denominator is the index.

a^()1 n=sqrt(a) and a^() m n=sqrt(a^m) Let's simplify the expression!

125^(43)

MoveNumRight

a/b=1/b* a

125^(13 * 4)

ProdInExponent

a^(m* n)=(a^m)^n

(125^(13))^4

PowToRootD

a^(1n)=sqrt(a)

(sqrt(125))^4

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