Question

Represent the expression (a⁵*a/a⁻³)⁻¹ as a power of a, where a is not equal to 0?

Answer 1

The expression (a⁵*a/a⁻³)⁻¹ can be simplified by using exponent rules to a⁹ and then applying the negative exponent rule to get the final answer, which is a⁻⁹.

Step-by-step explanation:

To represent the expression (a⁵*a/a⁻³)⁻¹ as a power of a, where a is not equal to 0, we need to apply the rules for dealing with exponents.

Firstly, according to the rules of exponents, when you multiply expressions with the same base, you add the exponents, so a⁵ * a is a⁶ (5 + 1 = 6). When you divide, you subtract the exponents, so a⁶ / a⁻³ is a⁹ (6 - (-3) = 9), according to rule A.6.

Using the rule from (A.9), a negative exponent indicates an inversion or putting the item in the denominator, so for instance, a⁻¹ would be 1/a.

Now, applying the negative exponent rule, the given expression (a⁵*a/a⁻³)⁻¹ becomes 1/a⁹.

Therefore, the expression (a⁵*a/a⁻³)⁻¹ represented as a power of a is a⁻⁹.