What is (4a^{-1}b^5c^{-3})^3 ?

The solution to (4a^{-1}b^5c^{-3})^3 is (64b^{15})/(a^3c^9)

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simplify (4a^{-1}b^5c^{-3})^3

simplify

(4 a^{- 1} b^{5} c^{- 3})^{3}

\frac{64 b ^{15}}{a ^{3} c ^{9}}

Solution steps

(4 a^{- 1} b^{5} c^{- 3})^{3}

Apply exponent rule:

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

(4 a^{- 1} b^{5} c^{- 3})^{3} = 4^{3} (a^{- 1})^{3} (b^{5})^{3} (c^{- 3})^{3}

= 4^{3} (a^{- 1})^{3} (b^{5})^{3} (c^{- 3})^{3}

4^{3} = 64

= 64 (a^{- 1})^{3} (b^{5})^{3} (c^{- 3})^{3}

Simplify

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

= 64 \cdot \frac{1}{a ^{3}} (b^{5})^{3} (c^{- 3})^{3}

Simplify

(b^{5})^{3} : b^{15}

= 64 \cdot \frac{1}{a ^{3}} b^{15} (c^{- 3})^{3}

Simplify

(c^{- 3})^{3} : \frac{1}{c ^{9}}

= 64 \cdot \frac{1}{a ^{3}} b^{15} \frac{1}{c ^{9}}

Simplify

64 \cdot \frac{1}{a ^{3}} b^{15} \frac{1}{c ^{9}} : \frac{64 b ^{15}}{a ^{3} c ^{9}}

= \frac{64 b ^{15}}{a ^{3} c ^{9}}

\frac{1 + \frac{4}{c - 4}}{1 - \frac{4}{c - 4}}

81 a^{2} - 16 = 0

4 p^{2} - (q + r)^{2}

\frac{3}{2} x + \frac{1}{5} \geq - 1

6 x^{2} + 18 x + 6

What is (4a^{-1}b^5c^{-3})^3 ?
The solution to (4a^{-1}b^5c^{-3})^3 is (64b^{15})/(a^3c^9)