Question

(q^4)^z=q^12
find the value of z

Answer 1

The value of z is 3.

Explanation:

You have to use Indices Law,

`{( {a}^(m)) }^(n) \: ⇒ \: {a}^(mn)`

So for this question, first you have to get rid of brackets :

`{ ({q}^(4) )}^(z) = {q}^(12)`

`{q}^(4z) = {q}^(12)`

Next you can solve it since both have the same bases :

`{q}^(4z) = {q}^(12)`

`4z = 12`

`z = 3`

Answer 2

z = 3

Explanation:

Using the rule of exponents

`(a^(m)) ^(n)` =
`a^(mn)`

Thus

`(q^(4)) ^(z)` =
`q^(4z)` , so

`q^(4z)` =
`q^(12)`

Since the bases on both sides are equal then equate the exponents

4z = 12 ( divide both sides by 4 )

z = 3