What is (sqrt((a^2b^{-3)c^5)/(ac^{-2)x}})^3 ?

The solution to (sqrt((a^2b^{-3)c^5)/(ac^{-2)x}})^3 is (ac^{10}sqrt(a)sqrt(c))/(b^4xsqrt(b)\sqrt{x)}

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simplify (sqrt((a^2b^{-3)c^5)/(ac^{-2)x}})^3

simplify

(\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{3}

\frac{a c ^{10} a c}{b ^{4} x b x}

Solution steps

(\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{3}

Apply exponent rule:

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

(\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{2 + 1} = (\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{2} \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x}

= (\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{2} \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x}

Apply exponent rule:

assuming

n i s o dd or a \geq 0

(\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x})^{2} = \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x}

= \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x} \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x}

Simplify

\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x} : \frac{c ^{3} a c}{b b x}

= \frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x} \cdot \frac{c ^{3} a c}{b b x}

Cancel

\frac{a ^{2} b ^{- 3} c ^{5}}{a c ^{- 2} x} : \frac{a c ^{7}}{b ^{3} x}

= \frac{a c ^{7}}{b ^{3} x} \cdot \frac{c ^{3} a c}{b b x}

Apply the fraction rule:

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

= \frac{a c ^{7} c ^{3} a c}{b ^{3} x b b x}

Simplify

c^{7} c^{3} : c^{10}

= \frac{a c ^{10} a c}{b ^{3} x b b x}

Simplify

b^{3} b : b^{4}

= \frac{a c ^{10} a c}{b ^{4} x b x}

1.5 \cdot 1 0^{- 2}

f (x) = e^{- \frac{1}{2} x}

What is (sqrt((a^2b^{-3)c^5)/(ac^{-2)x}})^3 ?
The solution to (sqrt((a^2b^{-3)c^5)/(ac^{-2)x}})^3 is (ac^{10}sqrt(a)sqrt(c))/(b^4xsqrt(b)\sqrt{x)}