What is (sqrt(25u^{-6)v^4})^3 ?

The solution to (sqrt(25u^{-6)v^4})^3 is (125v^6)/(u^9)

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simplify (sqrt(25u^{-6)v^4})^3

simplify

(25 u^{- 6} v^{4})^{3}

\frac{125 v ^{6}}{u ^{9}}

Solution steps

(25 u^{- 6} v^{4})^{3}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

(25 u^{- 6} v^{4})^{2 + 1} = (25 u^{- 6} v^{4})^{2} 25 u^{- 6} v^{4}

= (25 u^{- 6} v^{4})^{2} 25 u^{- 6} v^{4}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(25 u^{- 6} v^{4})^{2} = 25 u^{- 6} v^{4}

= 25 u^{- 6} v^{4} 25 u^{- 6} v^{4}

Simplify

25 u^{- 6} v^{4} : 5 \cdot \frac{1}{u ^{3}} v^{2}

= 25 u^{- 6} v^{4} \cdot 5 \cdot \frac{1}{u ^{3}} v^{2}

Multiply the numbers:

25 \cdot 5 = 125

= 125 u^{- 6} v^{4} \frac{1}{u ^{3}} v^{2}

Simplify

v^{4} v^{2} : v^{6}

= 125 u^{- 6} v^{6} \frac{1}{u ^{3}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

u^{- 6} = \frac{1}{u ^{6}}

= 125 \cdot \frac{1}{u ^{6}} v^{6} \frac{1}{u ^{3}}

Apply the fraction rule:

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

= \frac{125 \cdot 1 \cdot v ^{6} \cdot 1}{u ^{6} u ^{3}}

Multiply the numbers:

125 \cdot 1 \cdot 1 = 125

= \frac{125 v ^{6}}{u ^{6} u ^{3}}

Simplify

u^{6} u^{3} : u^{9}

= \frac{125 v ^{6}}{u ^{9}}

(3.4 x 1 0^{5}) (1.2 x 1 0^{- 3})

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e^{- (x + 1)}

\frac{6 , 0 \cdot 1 0 ^{24} \cdot 50}{640 0 ^{2}} \cdot 6.67 \cdot 1 0^{- 11}

(4 a^{2}) (6 a^{2})

What is (sqrt(25u^{-6)v^4})^3 ?
The solution to (sqrt(25u^{-6)v^4})^3 is (125v^6)/(u^9)