Answer:
The simplified form of given expression [tex](xyz^2)^4[/tex] is [tex]x^4y^4z^8[/tex]
Step-by-step explanation:
Given : Expression [tex](xyz^2)^4[/tex]
We have to write the simplified form the given expression [tex](xyz^2)^4[/tex]
Consider, The given expression [tex](xyz^2)^4[/tex]
Apply exponent rule, [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
We have,
[tex]=x^4y^4\left(z^2\right)^4[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}[/tex]
[tex]=z^{2\cdot \:4}=z^8[/tex]
Thus, [tex]=x^4y^4z^8[/tex]
Thus, The simplified form of given expression [tex](xyz^2)^4[/tex] is [tex]x^4y^4z^8[/tex]
