Which expression is equivalent to (StartFraction (2 a Superscript negative 3 Baseline b Superscript 4 Baseline) squared Over (3 a Superscript 5 Baseline b) Superscript negative 2 Baseline EndFraction) Superscript negative 1? Assume mc026-2.jpg.

Question

StartFraction 2 Over 3 a Superscript 4 Baseline b Superscript 10 Baseline EndFraction
StartFraction 4 Over 9 a Superscript 4 Baseline b Superscript 10 Baseline EndFraction
StartFraction 1 Over 36 a Superscript 4 Baseline b Superscript 10 Baseline EndFraction
StartFraction 36 a Superscript 4 Baseline b Superscript 10 Baseline EndFraction

Answer 1

To simplify the expression, we need to apply the power rule for exponents.

First, simplify the expression within the parentheses. We will apply the square to both the numerator and the denominator:

(2a^(-3)b^4)^2 = 2^2(a^(-3))^2(b^4)^2 = 4a^(-6)b^8

(3a^5b)^(-2) = (3^(-2))(a^5)^(-2)(b)^(-2) = 3^(-2)a^(-10)b^(-2)

Now, we can simplify the expression by taking the reciprocal:

(4a^(-6)b^8) / (3^(-2)a^(-10)b^(-2)) = 4a^(-6)b^8 * 3^2a^10b^2 = 12a^(-6+10)b^(8+2) = 12a^4b^10

Therefore, the equivalent expression is StartFraction 12 a Superscript 4 Baseline b Superscript 10 Baseline EndFraction.