Question

Which expression is equivalent to the one shown below?
(4z)^-3 x (2z)^5

Answer 1

`(1)/(2)\cdot z^2` is the required equivalent expression.

Explanation:

We have been given an expression:

`(4z)^(-3)\cdot (2z)^5`

First open the parenthesis and simplify we will get:

`(1)/(4^3\cdot z^3)\cdot 2^5\cdot z^5`

`(1)/(64z^3)\cdot 32z^5`

On simplification by dividing 64 by 32

`(1)/(2\cdot z^3)\cdot z^5`

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

`(1)/(2)\cdot z^(5-3)`

`(1)/(2)\cdot z^2` is the required equivalent expression.

Answer 2

Equivalent expression is
`(1)/(2)\cdot z^2`.

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)`=
`(1)/(a^(m) )`.

`(4z)^(-3)`*
`(2z)^(5)` =

`(2z)^(5)` *
`(1)/((4z)^(3) )`

We got
`(1)/((4z)^(3) )`*
`(2z)^(5)`.

On removing parenthesis

`(1)/(64z^3)\cdot 32z^5`.

On dividing 64 by 32

`(1)/(2\cdot z^3)\cdot z^5`.

By the quotient rule of exponent

`(a^(m) )/(a^(n))` =
`a^(m-n)`.

`(1)/(2)\cdot z^(5-3)`.

`(1)/(2)\cdot z^2`.

Therefore, Equivalent expression is
`(1)/(2)\cdot z^2`.