Question

Simplify. (z⁻⁷)/(z⁻³) Write vour answer with a positive exponent only.

Answer 1

The expression (z⁻⁷)/(z⁻³) simplifies to z⁻⁴, which, when converted to positive exponent form, is 1/z⁴.

Step-by-step explanation:

To simplify the expression (z⁻⁷)/(z⁻³), we need to use the rules of dividing exponents. The rule tells us to subtract the exponent in the denominator from the exponent in the numerator.

So, we take -7 (the exponent on the numerator) and subtract -3 (the exponent on the denominator):

-7 - (-3) = -7 + 3 = -4.

Therefore, the simplified expression is z⁻⁴. However, as we need to write our answer with a positive exponent only, we remember that a negative exponent indicates the reciprocal. This means that z⁻⁴ is equivalent to 1/z⁴. Thus, our final expression with a positive exponent is:

1/z⁴