Question

Represent the following as a power of a where a doesn't equal 0 (a³*a/a²)⁻¹

Answer 1

The expression (a³*a/a²)⁻¹ simplifies to a² inside the parentheses, and then applying the external exponent of -1 yields the final answer of a⁻².

Step-by-step explanation:

To represent (a³*a/a²)⁻¹ as a power of a where a does not equal 0, we must apply the rules of exponents. We'll use these rules:

• When multiplying powers with the same base, add the exponents (am * an = am+n).
• When dividing powers with the same base, subtract the exponents (am / an = am-n).
• A negative exponent means the reciprocal of the base raised to the positive of the exponent (a⁻¹ = 1/a).
• When an expression with an exponent is raised to another power, multiply the exponents ((an)m = an*m).

First, we simplify the expression inside the parentheses:

a³ * a¹/a² = a³+1-2 = a²

Then, we handle the external exponent of -1:

(a²)⁻¹ = a²*-1 = a⁻²

Thus, the expression (a³*a/a²)⁻¹ can be represented as a⁻².