Answer:
z = 3
Step-by-step explanation:
Using the rule of exponents
[tex](a^{m}) ^{n}[/tex] = [tex]a^{mn}[/tex]
Thus
[tex](q^{4}) ^{z}[/tex] = [tex]q^{4z}[/tex] , so
[tex]q^{4z}[/tex] = [tex]q^{12}[/tex]
Since the bases on both sides are equal then equate the exponents
4z = 12 ( divide both sides by 4 )
z = 3
Answer:
The value of z is 3.
Step-by-step explanation:
You have to use Indices Law,
[tex] {( {a}^{m}) }^{n} \: ⇒ \: {a}^{mn} [/tex]
So for this question, first you have to get rid of brackets :
[tex] { ({q}^{4} )}^{z} = {q}^{12} [/tex]
[tex] {q}^{4z} = {q}^{12} [/tex]
Next you can solve it since both have the same bases :
[tex] {q}^{4z} = {q}^{12} [/tex]
[tex]4z = 12[/tex]
[tex]z = 3[/tex]
