Question

Represent the following expressions as a power of a where a ≠ 0. (a²·a³ ·(a⁻¹))²

Answer 1

To represent (a² · a³ · (a⁻¹))² as a power of 'a', multiply the exponents within the parentheses to get a⁴, and then square the result to obtain a¸.

Step-by-step explanation:

The expression provided is (a² · a³ · (a⁻¹))². To simplify and represent this as a power of a, we use the properties of exponents. We start by multiplying the exponents inside the parentheses. Then, we apply the power of a product rule which states that (a·b)² = a²·b², so each term inside the parentheses has its exponent doubled when the entire expression is squared.

Step-by-step, it looks like this:

1. Multiply the exponents of a inside the parentheses: a² · a³ · a⁻¹ = a²+3⁻¹ = a⁴.
2. Now apply the power to the product to square the result: (a⁴)² = a⁴·² = a¸.

The final expression as a power of a, where a ≠ 0, is a¸.