Question

Represent the following expressions as a power of the number a (a≠0): ((a²)⁻¹)⁻¹ / (a/a⁻¹)²

a) a⁵
b) a⁻⁵
c) a⁻¹
d) a

Answer 1

The given expression simplifies to a⁻², which is none of the provided options. It appears there is an error with the answer choices.

Step-by-step explanation:

The expression given can be simplified using the properties of exponents:

((a²)⁻¹)⁻¹ / (a/a⁻¹)²

First, let's simplify the numerator:

• 
  
• ((a²)⁻¹)⁻¹ becomes a², since the double negative exponent means we're undoing the power of -1.

Next, we'll simplify the denominator:

Therefore, we have:

a² / a⁴

To simplify this division, we subtract the exponents: 2 - 4 equals -2.

So, the simplified expression is a⁻².

However, none of the given options (a) a⁵, (b) a⁻⁵, (c) a⁻¹, (d) a, corresponds to the correct result a⁻². There seems to be a mistake with the given options.