Solve using positive exponents only.

Question

(4x^-3y^2)-2

(5a-^3/4a-^5)^3

Answer 1

a).

The expression is (4x^{- 3}y²)^{- 2}.

Apply negative exponent property : a^-n = 1/aⁿ, where a ≠ 0.

(4x^{- 3}y²)^{- 2} = 1/(4x^{- 3}y²)²

Again apply negative exponent property : a^-n = 1/aⁿ, where a ≠ 0.

= 1/((4/x³)y²)²

= 1/(4y²/x³)²

Power of a Power Property : (a^m)ⁿ = a^mn.

= 1/(16y⁴/x⁶)

= x⁶/16y⁴ .

Answer 2

b).

The expression is (5a^{- 3}/4a^{- 5})³.

Apply negative exponent property : a^-n = 1/aⁿ, where a ≠ 0.

(5a^{- 3}/4a^{- 5})³ = [(5/a³)/(4/a⁵)]³

= [(5 * a⁵)/(4 * a³)]³

= [(5 * a³ * a²)/(4 * a³)]³

Cancel common terms.

= [(5a²)/4]³ 

Power of a Power Property : (a^m)ⁿ = a^mn.

= 125a⁶/64.