Explain how writing x to the power of negative 7 end exponent with positive exponents is similar to writing x to the power of negative 1 divided by 4 end exponent with positive exponents.

Question

explain and show work please

Answer 1

x⁻⁷=1/x⁷ and x^-¼=1/x^¼. In each case, we get the positive exponent by writing down the inverse of the quantity. The reason for this is that x^y×x^(-y)=x^(y-y)=x⁰=1, so x^(-y)=1/x^y We simply apply the rule of adding exponents when we multiply and subtracting them when we divide.