TestU11403767816
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# Evaluate. fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 5 to the power of negative 1 over 6 5 to the power of 3 over 2 9 92

The answer is 1/3 To calculate this will use several rules: $\sqrt[n]{x^m } = x^{ \frac{m}{n} }$ $x^{-m}= \frac{1}{ x^{m} }$ $x^{a} * x^{b} =x ^{a+b}$ $\frac{ x^{a} }{ x^{b} } = x^{a-b}$ The fourth root of 9 is $\sqrt[4]{9}= \sqrt[4]{ 9^{1} }= 9^{ \frac{1}{4} }$ Square root of 9 is $\sqrt[2]{9}= \sqrt[2]{ 9^{1} } = 9^{ \frac{1}{2} }$ The fourth root of 9 to the power of 5 is $\sqrt[4]{9^{5} } = 9^{ \frac{5}{4} }$ The fourth root of 9 multiplied by square root of 9 over the fourth root of 9 to the power of 5 is: $\frac{9^{ \frac{1}{4} }*9^{ \frac{1}{2} }}{9^{ \frac{5}{4} }} = \frac{ 9^{ \frac{1}{4}+ \frac{1}{2}} }{9 \frac{5}{4} } =9^{ \frac{1}{4}+ \frac{1}{2}- \frac{5}{4} }=9^{ \frac{1}{4}+ \frac{1*2}{2*2}- \frac{5}{4} }=9^{ \frac{1}{4}+ \frac{2}{4}- \frac{5}{4} }=9^{ \frac{1+2-5}{4} }= 9^{ \frac{-2}{4} }$ $= 9^{- \frac{1}{2} }= \frac{1}{9^{ \frac{1}{2} } } =\frac{1}{ \sqrt[2]{9^{1} } } = \frac{1}{ \sqrt[2]{9} } = \frac{1}{3}$