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Core Connections Integrated I, 2013 View details

1. Section 5.1

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Exercise 13 Page 251

a To simplify the given expression, we will use the quotient rule of exponents,

a^{m} \cdot a^{n} = a^{m + n} .

\frac{5 ^{723}}{5 ^{721}}

DivPow

$\frac{a ^{m}}{a ^{n}} = a^{m - n}$

5^{723 - 721}

SubTerms

Subtract terms

5^{2}

CalcPow

Calculate power

25

b Again, we will use the quotient rule of exponents,

\frac{a ^{m}}{a ^{n}} = a^{m - n} .

\frac{3 ^{300}}{3 ^{249}}

DivPow

$\frac{a ^{m}}{a ^{n}} = a^{m - n}$

3^{300 - 249}

SubTerms

Subtract terms

3^{51}

c Notice that the exterior power is zero

(0) .

Since any non-zero number raised to zero equals one, we do not need to simplify the fraction between the parentheses to know the final result.

(\frac{3 \cdot 4 ^{3}}{3 ^{- 2} \cdot 4 ^{- 7}})^{0} = 1

d Finally, we will use the quotient rule of exponents to simplify the expression between the brackets. Then, we will apply the power rule of exponents,