What is (((49a^{-8}))/((25b^6)))^{21/2} ?

The solution to (((49a^{-8}))/((25b^6)))^{21/2} is (7^{21})/(5^{21)a^{84}b^{63}}

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simplify (((49a^{-8}))/((25b^6)))^{21/2}

simplify

(\frac{( 49 a ^{- 8} )}{( 25 b ^{6} )})^{\frac{21}{2}}

\frac{7 ^{21}}{5 ^{21} a ^{84} b ^{63}}

Solution steps

(\frac{49 a ^{- 8}}{25 b ^{6}})^{\frac{21}{2}}

Apply exponent rule:

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

= \frac{( 49 a ^{- 8} ) ^{\frac{21}{2}}}{( 25 b ^{6} ) ^{\frac{21}{2}}}

Simplify

(49 a^{- 8})^{\frac{21}{2}} : \frac{7 ^{21}}{a ^{84}}

= \frac{\frac{7 ^{21}}{a ^{84}}}{( 25 b ^{6} ) ^{\frac{21}{2}}}

Simplify

(25 b^{6})^{\frac{21}{2}} : 5^{21} b^{63}

= \frac{\frac{7 ^{21}}{a ^{84}}}{5 ^{21} b ^{63}}

Apply the fraction rule:

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

= \frac{7 ^{21}}{5 ^{21} a ^{84} b ^{63}}

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What is (((49a^{-8}))/((25b^6)))^{21/2} ?
The solution to (((49a^{-8}))/((25b^6)))^{21/2} is (7^{21})/(5^{21)a^{84}b^{63}}