Would the problem (xz^3)^-4 be simplified to 1/x4z12?

yes

1
------------
x^4 z^12

which is

x^-4 z^-12

PS

I hope you got my note about the previous question. Only combine LIKE terms !

Yes, thank you. I had the answer you wrote but wasn't sure.

To simplify the expression (xz^3)^-4, we can apply the exponent to both the variable x and the variable z^3 separately.

When raising a power to another power, we multiply the exponents. In this case, we have (xz^3)^-4, so we apply the exponent -4 to both x and z^3.

Let's simplify:

For x: (x^-4) = 1/x^4

For z^3: (z^3)^-4 = z^(3 * -4) = z^-12

Now, we can substitute these simplified expressions back into the original equation:

(xz^3)^-4 = (1/x^4)(z^-12)

Since the variables x and z have different exponents, we cannot combine them into a single expression. So, the simplified expression is:

(1/x^4)(z^-12)

Note that z^-12 is equivalent to 1/z^12, so we can write the expression as:

1/(x^4 * z^12)