Question

Write each expression as a power of a where a is not equal to 0. (a⁻¹*a⁻²)⁻¹

Answer 1

The expression (a^(-1)*a^(-2))^(-1) simplifies to a^3 using the rules of exponents, specifically by adding exponents when multiplying like bases and multiplying exponents when raising a power to a power.

Step-by-step explanation:

The expression (a⁻¹*a⁻²)⁻¹ can be simplified using the rules of exponents. First, we apply the rule of multiplication which states that when multiplying exponential expressions with the same base, we add the exponents. This turns our expression into a⁻¹⁻². Secondly, applying the power of a power rule, we multiply the exponents, resulting in a³. Therefore, the expression written as a power of a where a is not equal to 0 is a³.