Question

Which expression is equivalent to The equation

Answer 1

Answer: last option.

Step-by-step explanation:

 The negative exponent rules establishes the following:

$a^{-n}=\frac{1}{a^n}$

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:

$(\frac{1}{x^2*x^6})^3=(\frac{1}{x^8})^3=\frac{1}{x^{24}}$

Therefore the answer is the last option.

Answer 2

Answer:

The correct answer is last option 1/x²⁴

Step-by-step 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