Question

Represent the following expressions as a power of the number a (a≠0): (a ⋅ a² ⋅ a³)/(a/a²)⁻¹

a) a⁹
b) a³
c) a⁻³
d) a⁻⁹

Answer 1

To represent the given expression as a power of the number a, simplify it by breaking it down step by step. The expression (a ⋅ a² ⋅ a³)/(a/a²)⁻¹ simplifies to a⁹.

Step-by-step explanation:

To represent the given expression as a power of the number a, we need to simplify it. Let's break it down step by step:

(a ⋅ a² ⋅ a³)/(a/a²)⁻¹

First, simplify the expression inside the brackets: (a/a²)⁻¹ = (a⋅a²)⁻¹ = 1/(a⋅a²) = 1/a³

Now, substitute the simplified expression back into the original expression: (a ⋅ a² ⋅ a³)/(1/a³) = a ⋅ a² ⋅ a³ ⋅ a³ = a⁹

Therefore, the expression (a ⋅ a² ⋅ a³)/(a/a²)⁻¹ is equal to a⁹.