Question

Mario simplified the expression (4 z Superscript 8 Baseline) Superscript negative 3 as shown. (4 z Superscript 8 Baseline) Superscript negative 3 = 4 z Superscript 8 times (negative 3) Baseline = 4 z Superscript negative 24 Baseline = StartFraction 4 Over z Superscript 24 Baseline EndFraction Which statement explains Mario's error?

Answer 1

Explanation:

Given the expression
`(4z^8)^(-3)`, to evaluate this, we will use one of the law of indices as shown;

`(a^m)^n = a^(mn)`

`4^(-3) * z^(8*-3)`

`= (1)/(4^3) * z^(-24)\\ \\= (1)/(64) * (1)/(z^(24))\\ \\= (1)/(64z^(24))`

Mario's error was that she did not raise the value of 4 to the power of -3. She only raised z^8 to the power of -3 when it is supposed to affect both 4 and z^8