Question

Write (8a^3)^ -2/3 in simplest form.
All steps are needed!!

Answer 1

Answer:1/(2a)^2
Steps:
(8a^3)^ -2/3
=1/(8a^3)^ 2/3
=1/(2^3 × a^3)^ 2/3
=1/(2a)^3×2/3
=1/(2a)^2

Answer 2

To write (8a³)⁻²/₃ in simplest form, we have that (8a³)⁻²/₃ = 1/(4a²)

To write (8a³)⁻²/₃ in simplest form, we proceed as follows

Since we have the expression (8a³)⁻²/₃ in exponent form. Using the reciprocal law of exponents which states that x⁻ⁿ = 1/xⁿ, So, we have that

(8a³)⁻²/₃= 1/(8a³)²/₃

Now using the root rule of exponents which is xᵃ/ₙ = (ⁿ√x)ᵃ. So, we have that

1/(8a³)²/₃ = 1/[³√(8a³)]²

Separating the cube roots, we have that

= 1/[³√8 ׳√a³)]²

= 1/[2 × a]²

= 1/[2a]²

= 1/(4a²)

So, (8a³)⁻²/₃ = 1/(4a²)