What is ((a^3)/(ab^{-6)})^{1/2} ?

The solution to ((a^3)/(ab^{-6)})^{1/2} is ab^3

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simplify ((a^3)/(ab^{-6)})^{1/2}

simplify

(\frac{a ^{3}}{a b ^{- 6}})^{\frac{1}{2}}

a b^{3}

Solution steps

(\frac{a ^{3}}{a b ^{- 6}})^{\frac{1}{2}}

Apply exponent rule:

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

= \frac{( a ^{3} ) ^{\frac{1}{2}}}{( a b ^{- 6} ) ^{\frac{1}{2}}}

Simplify

(a^{3})^{\frac{1}{2}} : a^{\frac{3}{2}}

= \frac{a ^{\frac{3}{2}}}{( a b ^{- 6} ) ^{\frac{1}{2}}}

Simplify

(a b^{- 6})^{\frac{1}{2}} : \frac{a ^{\frac{1}{2}}}{b ^{3}}

= \frac{a ^{\frac{3}{2}}}{\frac{a ^{\frac{1}{2}}}{b ^{3}}}

Apply the fraction rule:

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

= \frac{a ^{\frac{3}{2}} b ^{3}}{a ^{\frac{1}{2}}}

Apply exponent rule:

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

\frac{a ^{\frac{3}{2}}}{a ^{\frac{1}{2}}} = a^{\frac{3}{2} - \frac{1}{2}}

= b^{3} a^{\frac{3}{2} - \frac{1}{2}}

Subtract the numbers:

\frac{3}{2} - \frac{1}{2} = 1

= a b^{3}

43 = 1.14 X

0.9 < 3 x + 2.4 < 6.9

7 (x - 1) - 6 (x + 1) = 3 x - 21

x^{2} = 6 - x

4 x^{2} - 16 x + 7 = 0

What is ((a^3)/(ab^{-6)})^{1/2} ?
The solution to ((a^3)/(ab^{-6)})^{1/2} is ab^3