Question

Simplify: (2^0a^-3b^4z^2)^-4 and show all work.

Answer 1

To simplify the expression (2^0a^-3b^4z^2)^-4, apply the negative exponent to each term inside the parentheses and simplify the resulting expression.

Step-by-step explanation:

To simplify the expression (2^0a^-3b^4z^2)^-4, we can use the rule that states a^m^n = a^(m*n). In this case, the exponent outside the parentheses (-4) is applied to each term inside the parentheses. So we have:

(2^0)^-4 * (a^-3)^-4 * (b^4)^-4 * (z^2)^-4

Any number raised to the power of 0 equals 1, and applying the negative exponent flips the fraction, so we get:

1^-4 * a^12 * b^-16 * z^-8

Finally, any number raised to the power of -n is equal to its reciprocal raised to the power of n. So we have:

1 * a^12 * (1/b^16) * (1/z^8) = a^12 / (b^16 * z^8)