Question 202699
If the problem is {{{-6z^(-4)}}}, then the correct way to read this is: "negative six times z to the negative fourth power" or "negative six times z to the power of negative four". And the only way to simplify this is to write it with a positive exponent. Using the fact that {{{a^(-n) = 1/(a^n)}}}, we get {{{(-6)/(z^4)}}}.<br>
If the problem is "negative 6z to the power of negative 4", then the correct way to write this is {{{(-6z)^(-4)}}}. Note the parentheses! They are critical. Exponent only apply to whatever is <b>immediately</b> in front of them! With the right parenthesis in front of the exponent, the exponent applies to the entire expression in the parentheses. Without the parentheses the exponent only applies to the z.<br>
To simplify {{{(-6z)^(-4)}}} we can start by using the {{{a^(-n) = 1/(a^n)}}} property to give: {{{1/((-6z)^4)}}}. Then we can use the property {{{(a*b)^n = a^n * b^n}}} to give: {{{1/((-6)^4 * z^4)}}}. Since {{{(-6)^4 = 1296}}} we get {{{1/(1296z^4)}}}. (If negative exponents are allowed, then this could alos be written as {{{z^(-4)/1296}}} or {{{(1/1296)z^(-4)}}}).