What is (2^{-4}*z^{-3})^5 ?

The solution to (2^{-4}*z^{-3})^5 is 1/(1048576z^{15)}

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simplify (2^{-4}*z^{-3})^5

simplify

(2^{- 4} \cdot z^{- 3})^{5}

\frac{1}{1048576 z ^{15}}

Solution steps

(2^{- 4} z^{- 3})^{5}

Apply exponent rule:

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

(2^{- 4} z^{- 3})^{5} = (2^{- 4})^{5} (z^{- 3})^{5}

= (2^{- 4})^{5} (z^{- 3})^{5}

(2^{- 4})^{5} = \frac{1}{1048576}

= \frac{1}{1048576} (z^{- 3})^{5}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

(z^{- 3})^{5} = z^{- 3 \cdot 5}

= \frac{1}{1048576} z^{- 3 \cdot 5}

Multiply the numbers:

3 \cdot 5 = 15

= \frac{1}{1048576} z^{- 15}

Apply exponent rule:

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

z^{- 15} = \frac{1}{z ^{15}}

= \frac{1}{1048576} \cdot \frac{1}{z ^{15}}

Simplify

\frac{1}{1048576} \cdot \frac{1}{z ^{15}} : \frac{1}{1048576 z ^{15}}

= \frac{1}{1048576 z ^{15}}

\frac{- 15 k ^{2}}{15 k ^{3} + 45 k ^{2}}

- 3 x + 2 > 17 or - 5 x + 3 \leq 13

8 x + 4 (- 6 x + 4) = - 6 - 5 x

4 = - 2 (x + 3)

\frac{- 5 - 2 i}{4 + 3 i}

What is (2^{-4}*z^{-3})^5 ?
The solution to (2^{-4}*z^{-3})^5 is 1/(1048576z^{15)}