What is (a^{-1}b^{1/3}*a^{-4/3}b^2)^2 ?

The solution to (a^{-1}b^{1/3}*a^{-4/3}b^2)^2 is ((b^{14})/(a^{14)})^{1/3}

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simplify (a^{-1}b^{1/3}*a^{-4/3}b^2)^2

simplify

(a^{- 1} b^{\frac{1}{3}} \cdot a^{- \frac{4}{3}} b^{2})^{2}

(\frac{b ^{14}}{a ^{14}})^{\frac{1}{3}}

Solution steps

(a^{- 1} b^{\frac{1}{3}} a^{- \frac{4}{3}} b^{2})^{2}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(a^{- 1} b^{\frac{1}{3}} a^{- \frac{4}{3}} b^{2})^{2} = (a^{- 1})^{2} (b^{\frac{1}{3}})^{2} (a^{- \frac{4}{3}})^{2} (b^{2})^{2}

= (a^{- 1})^{2} (b^{\frac{1}{3}})^{2} (a^{- \frac{4}{3}})^{2} (b^{2})^{2}

Simplify

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

= \frac{1}{a ^{2}} (b^{\frac{1}{3}})^{2} (a^{- \frac{4}{3}})^{2} (b^{2})^{2}

Simplify

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

= \frac{1}{a ^{2}} b^{\frac{2}{3}} (a^{- \frac{4}{3}})^{2} (b^{2})^{2}

Simplify

(a^{- \frac{4}{3}})^{2} : \frac{1}{a ^{\frac{8}{3}}}

= \frac{1}{a ^{2}} b^{\frac{2}{3}} \frac{1}{a ^{\frac{8}{3}}} (b^{2})^{2}

Simplify

(b^{2})^{2} : b^{4}

= \frac{1}{a ^{2}} b^{\frac{2}{3}} \frac{1}{a ^{\frac{8}{3}}} b^{4}

Apply exponent rule:

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

b^{\frac{2}{3}} b^{4} = b^{\frac{2}{3} + 4}

= \frac{1}{a ^{2}} \cdot \frac{1}{a ^{\frac{8}{3}}} b^{\frac{2}{3} + 4}

b^{\frac{2}{3} + 4} = b^{\frac{14}{3}}

= \frac{1}{a ^{2}} \cdot \frac{1}{a ^{\frac{8}{3}}} b^{\frac{14}{3}}

Multiply fractions:

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

= \frac{1 \cdot 1 \cdot b ^{\frac{14}{3}}}{a ^{2} a ^{\frac{8}{3}}}

Multiply:

1 \cdot 1 \cdot b^{\frac{14}{3}} = b^{\frac{14}{3}}

= \frac{b ^{\frac{14}{3}}}{a ^{2} a ^{\frac{8}{3}}}

a^{2} a^{\frac{8}{3}} = a^{2 + \frac{8}{3}}

= \frac{b ^{\frac{14}{3}}}{a ^{2 + \frac{8}{3}}}

a^{2 + \frac{8}{3}} = a^{\frac{14}{3}}

= \frac{b ^{\frac{14}{3}}}{a ^{\frac{14}{3}}}

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

= (\frac{b ^{14}}{a ^{14}})^{\frac{1}{3}}

y^{3} \cdot y^{- 5}

46 = - 6 t - 8

\frac{2 - 2 x}{3 x - 6} \leq 1

- 2 < - 4 z + 2 \leq 14

w^{2} + 32 = 0

What is (a^{-1}b^{1/3}*a^{-4/3}b^2)^2 ?
The solution to (a^{-1}b^{1/3}*a^{-4/3}b^2)^2 is ((b^{14})/(a^{14)})^{1/3}