Answer:
[tex]\frac{1}{2}\cdot z^2[/tex] is the required equivalent expression.
Step-by-step explanation:
We have been given an expression:
[tex](4z)^{-3}\cdot (2z)^5[/tex]
First open the parenthesis and simplify we will get:
[tex]\frac{1}{4^3\cdot z^3}\cdot 2^5\cdot z^5[/tex]
[tex]\frac{1}{64z^3}\cdot 32z^5[/tex]
On simplification by dividing 64 by 32
[tex]\frac{1}{2\cdot z^3}\cdot z^5[/tex]
When positive power changes its position from denominator to numerator its sign changes and vice-versa.
[tex]\frac{1}{2}\cdot z^{5-3}[/tex]
[tex]\frac{1}{2}\cdot z^2[/tex] is the required equivalent expression.
Answer:
Equivalent expression is[tex]\frac{1}{2}\cdot z^2 [/tex].
Step-by-step explanation:
Given: [tex](4z)^{-3}[/tex]×[tex](2z)^{5}[/tex]
To find: Which expression is equivalent to the one shown below.
Solution: We have given that [tex](4z)^{-3}[/tex]×[tex](2z)^{5}[/tex].
By the negative exponent rule [tex]a^{-m}[/tex]=[tex]\frac{1}{a^{m} }[/tex].
[tex](4z)^{-3}[/tex]*[tex](2z)^{5}[/tex] =
[tex](2z)^{5}[/tex] *[tex]\frac{1}{(4z)^{3} }[/tex]
We got [tex]\frac{1}{(4z)^{3} }[/tex]*[tex](2z)^{5}[/tex].
On removing parenthesis
[tex]\frac{1}{64z^3}\cdot 32z^5[/tex].
On dividing 64 by 32
[tex]\frac{1}{2\cdot z^3}\cdot z^5[/tex].
By the quotient rule of exponent
[tex]\frac{a^{m} }{a^{n}}[/tex] = [tex]a^{m-n}[/tex].
[tex]\frac{1}{2}\cdot z^{5-3} [/tex].
[tex]\frac{1}{2}\cdot z^2 [/tex].
Therefore, Equivalent expression is [tex]\frac{1}{2}\cdot z^2 [/tex].
