Answer:
[tex]=256x^8y^{20}[/tex]
Step-by-step explanation:
We have the expression:
[tex](4x^2y^5)^4[/tex]
We can use the power of a product property:
[tex](ab)^x=a^xb^x[/tex]
This yields:
[tex]=(4)^4\cdot(x^2)^4\cdot(y^5)^4[/tex]
We can evaluate 4 to the fourth:
[tex]=256(x^2)^4\cdot(y^5)^4[/tex]
Now, we can use the power of a power property:
[tex](x^a)^b=x^{ab}[/tex]
So:
[tex]=256(x^{2(4)})(y^{5(4)})[/tex]
Multiply:
[tex]=256x^8y^{20}[/tex]
And we're done!
