Verified Answer :

Answer:

\(\frac{1}{2}\cdot z^2\) is the required equivalent expression.

Step-by-step explanation:

We have  been given an expression:

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

First open the parenthesis and simplify we will get:

\(\frac{1}{4^3\cdot z^3}\cdot 2^5\cdot z^5\)

\(\frac{1}{64z^3}\cdot 32z^5\)

On simplification by dividing 64 by 32

\(\frac{1}{2\cdot z^3}\cdot z^5\)

When positive power changes its position from denominator to numerator its sign changes and vice-versa.

\(\frac{1}{2}\cdot z^{5-3}\)

\(\frac{1}{2}\cdot z^2\) is the required equivalent expression.

Answer:

Equivalent expression is\(\frac{1}{2}\cdot z^2\).

Step-by-step explanation:

Given: \((4z)^{-3}\)×\((2z)^{5}\)

To find: Which expression is equivalent to the one shown below.

Solution: We have given that  \((4z)^{-3}\)×\((2z)^{5}\).

By the negative exponent rule \(a^{-m}\)=\(\frac{1}{a^{m} }\).

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

\((2z)^{5}\) \(\frac{1}{(4z)^{3} }\)

We got \(\frac{1}{(4z)^{3} }\)*\((2z)^{5}\).

On removing parenthesis

\(\frac{1}{64z^3}\cdot 32z^5\).

On dividing 64 by 32

\(\frac{1}{2\cdot z^3}\cdot z^5\).

By the quotient rule of exponent

\(\frac{a^{m} }{a^{n}}\) = \(a^{m-n}\).

\(\frac{1}{2}\cdot z^{5-3}\).

\(\frac{1}{2}\cdot z^2\).

Therefore, Equivalent expression is \(\frac{1}{2}\cdot z^2\).

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