Question

Which expression is equivalent to The equation

Answer 1

The correct answer is last option 1/x²⁴

Explanation:

Points to remember

1). (x)⁻ᵃ = 1/xᵃ

2). (xᵃ)ᵇ = xᵃᵇ

3). xᵃ/xᵇ = xᵃ⁻ᵇ

It is given that, { x⁻⁶/x² }³

To find the equivalent expression

{ x⁻⁶/x² }³ = (x⁻⁶ ⁻ ²)³

= (x⁻⁸)³

= x⁻²⁴

= 1/x²⁴

Therefore the correct answer is last option

{ x⁻⁶/x² }³ = 1/x²⁴

Answer 2

Answer: last option.

Explanation:

The negative exponent rules establishes the following:

`a^(-n)=(1)/(a^n)`

The power to power property establishes:

`(a^b)^c=a^(bc)`

The product of powers property establishes that when you multiply two powers with equal base you must add the exponents.

Applying the properties, you obtain the equivalent expression shown below:

`((1)/(x^2*x^6))^3=((1)/(x^8))^3=(1)/(x^(24))`

Therefore the answer is the last option.