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Rational Exponents and Radicals

Radical Functions

Rational Exponents and Radicals 1.19 - Solution

Return to Rational Exponents and Radicals

To simplify the given expression, we will use the properties of exponents. For this exercise, we will begin by distributing the exponent to the numerator and denominator. Then we will try to eliminate the exponent by splitting the terms into perfect cube factors. Let's do it!

(\frac{8 x ^{6}}{2 7 y ^{9}})^{\frac{1}{3}}

(\frac{a}{b})^{m} = \frac{a ^{m}}{b ^{m}}

\frac{( 8 x ^{6} ) ^{\frac{1}{3}}}{( 2 7 y ^{9} ) ^{\frac{1}{3}}}

(a \cdot b)^{m} = a^{m} \cdot b^{m}

\frac{( 8 ) ^{\frac{1}{3}} \cdot ( x ^{6} ) ^{\frac{1}{3}}}{( 2 7 ) ^{\frac{1}{3}} \cdot ( y ^{9} ) ^{\frac{1}{3}}}

WritePowWrite as a power

\frac{( 2 ^{3} ) ^{\frac{1}{3}} \cdot ( x ^{6} ) ^{\frac{1}{3}}}{( 3 ^{3} ) ^{\frac{1}{3}} \cdot ( y ^{9} ) ^{\frac{1}{3}}}

(a^{m})^{n} = a^{m \cdot n}

\frac{2 ^{3 \cdot \frac{1}{3}} \cdot x ^{6 \cdot \frac{1}{3}}}{3 ^{3 \cdot \frac{1}{3}} \cdot y ^{9 \cdot \frac{1}{3}}}

MoveLeftFacToNumOne

a \cdot \frac{1}{b} = \frac{a}{b}

\frac{2 ^{\frac{3}{3}} \cdot x ^{\frac{6}{3}}}{3 ^{\frac{3}{3}} \cdot y ^{\frac{9}{3}}}

CalcQuotCalculate quotient

\frac{2 ^{1} \cdot x ^{2}}{3 ^{1} \cdot y ^{3}}

a^{1} = a

\frac{2 \cdot x ^{2}}{3 \cdot y ^{3}}

MultiplyMultiply

\frac{2 x ^{2}}{3 y ^{3}}