Without using (10), show directly that (10.6^-1) ^8=17.6^-8

We are given the expression:

(17.6^-1) ^8 = 17.6 ^ - 8

This means that the two terms on each side are equal. We are asked to show how this is possible.

First, use the rule of exponents. If a term raised to the power of a number x^n and is further raised to the power m: (x^n) ^m, to simplify the expression, multiply n and m and this will be your end exponent = x^nm.

We can apply this rule here:

17.6^-1 ^ 8

-1 * 8 = - 8

then, retain the base and replace the exponent with the product nm:

17.6 ^-8. This proves that the left term is equal to the right term.