Question

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

Answer 1

Answer:

z = 3

Step-by-step 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

Answer 2

Answer:

The value of z is 3.

Step-by-step 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 :

${q}^{4z} = {q}^{12}$

$4z = 12$

$z = 3$