Question

Represent the following expressions as a power of the number a (a≠0): (a⁻¹ x a⁻²)⁻³

a) a⁹
b) a⁻⁹
c) a⁻⁶
d) a⁶

Answer 1

The expression (a⁻¹ × a⁻²)⁻³ simplifies to a⁻⁹, by using the properties of exponents, where the exponents are added when multiplying powers with the same base and multiplied when raising a power to a power.

Step-by-step explanation:

The expression given is (a⁻¹ × a⁻²)⁻³. To simplify this, we will use the properties of exponents. First, notice that when we multiply powers with the same base, we add the exponents.

So, a⁻¹ × a⁻² becomes a⁻¹⁻² or a⁻³. Next, when we raise a power to a power, we multiply the exponents. Thus, (a⁻³)⁻³ simplifies to a⁻¹, because ⁻³ × ⁻³ = 9. The correct representation of the original expression in the form of a power of the number a is a⁻¹, which corresponds to option b) a⁻⁹.