Question

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

Answer 1

Answer:

Option (c) is correct.

$8z^2$ is the  equivalent  expression to $4z^{-3}\times 2z^5$

Step-by-step explanation:

Given expression $4z^{-3}\times 2z^5$

We have to find an equivalent fraction and choose one from the options given.

Consider the given expression $4z^{-3}\times 2z^5$

Apply exponent rule, $\:a^{-b}=\frac{1}{a^b}$

$z^{-3}=\frac{1}{z^3}$

We have,

$=4\times \:2\times \frac{1}{z^3}z^5$

Now, multiply fractions $a\times \frac{b}{c}=\frac{a\:\times \:b}{c}$

$=\frac{1\times \:4\times \:2z^5}{z^3}$

we have, $=\frac{8z^5}{z^3}$

Apply exponent rules, $\frac{x^a}{x^b}\:=\:x^{a-b}$

We have,

$\frac{z^5}{z^3}=z^{5-3}=z^2$

$4z^{-3}\times 2z^5=8z^2$

Thus, $8z^2$ is the  equivalent  expression to $4z^{-3}\times 2z^5$

Option (c) is correct.

Answer 2

I hope this helps you



4z^-3.2z^5



4.2.z^-3+5


8.z^2