Question

Represent the expression (a⁵ ⋅ a ÷ a⁻³)⁻¹ as a power of a, where a ≠0.a

a) a⁻⁷
b) a⁻⁵
c) a⁷
d) a⁵

Answer 1

The expression (a⁵ · a ÷ a⁻³)⁻¹ simplifies to a⁻³, following the rules of exponents. However, this result is not listed among the provided options, suggesting a possible error in the options or in the original expression.

Step-by-step explanation:

To represent the expression (a⁵ · a ÷ a⁻³)⁻¹ as a power of a, where a ≠ 0, we will apply the rules of exponents. First, we multiply exponents of terms with the same base when dividing, and then we raise a power to a power by multiplying the exponents.

Starting with a⁵ · a ÷ a⁻³, we have:

• a⁵ · a is a⁵¹, so we add the exponents: a⁶.
• When we divide by a⁻³, we subtract the exponent from the numerator, giving us a⁶⁻³, which simplifies to a³.

Now, we take the inverse of this expression, because of the exponent ⁻¹:

• (a³)⁻¹ means we multiply the exponents 3 and ⁻¹, resulting in a³×⁻¹ = a⁻³.

The correct representation as a power of a is thus a⁻³, which is not among the options provided. It looks like there might be an error in the options or in the original expression, as none of the answer choices (a⁻⁷, a⁻⁵, a⁷, a⁵) match the calculated result of a⁻³.