Question

Which expression is equivalent to (StartFraction (3 x y Superscript negative 5 Baseline) cubed Over (x Superscript negative 2 Baseline y squared) Superscript negative 4 Baseline) EndFraction) Superscript negative 2? Assume StartFraction x Superscript 10 Baseline y Superscript 14 Baseline Over 729 EndFraction.
StartFraction x Superscript 10 Baseline y Superscript 14 Baseline Over 729 EndFraction
StartFraction x Superscript 22 Baseline Over 18 y Superscript 46 Baseline EndFraction
StartFraction 729 Over x Superscript 10 Baseline y Superscript 14 Baseline EndFraction
StartFraction 18 y Superscript 46 Baseline Over x Superscript 22 Baseline EndFraction

Answer 1

Option a: $\frac{x^{10} y^{14}}{729}$ is the correct answer.

Explanation:

The expression is $\left(\frac{\left(3 x y^{-5}\right)^{3}}{\left(x^{-2} y^{2}\right)^{-4}}\right)^{-2}$

We shall simplify the expression, to determine the expression which is equivalent to $\left(\frac{\left(3 x y^{-5}\right)^{3}}{\left(x^{-2} y^{2}\right)^{-4}}\right)^{-2}$

Multiplying the powers, we get,

$\left(\frac{\left3^{3} x^{3} y^{-15}\right}{x^{8} y^{-8}}\right)^{-2}$

Again multiplying the powers, we get,

$\left\frac{\left3^{-6} x^{-6} y^{30}\right}{x^{-16} y^{16}}\right$

Dividing the fractions, we have,

$\left\frac{\left3^{-6} y^{14}\right}{x^{-10} }\right$

Applying the exponent rule, $a^{-b}=\frac{1}{a^{b}}$, we have,

$\frac{x^{10} y^{14}}{3^{6} }$

Hence, the expression can be written as

$\frac{x^{10} y^{14}}{729}$

Thus, the expression which is equivalent to $\left(\frac{\left(3 x y^{-5}\right)^{3}}{\left(x^{-2} y^{2}\right)^{-4}}\right)^{-2}$ is $\frac{x^{10} y^{14}}{729}$

Hence, Option a is the correct answer.

Answer 2

A.)‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎‎