Which expression is equivalent to StartFraction (3 m Superscript negative 2 Baseline n) Superscript negative 3 Baseline Over 6 m n Superscript negative 2 Baseline EndFraction? Assume m not-equals 0, n not-equals 0.
StartFraction m Superscript 5 Baseline Over 162 n EndFraction
StartFraction 1 Over 2 m cubed n EndFraction
StartFraction 8 m Superscript 9 Baseline Over n Superscript 9 Baseline EndFraction
StartFraction 4 m Superscript 8 Baseline Over 3 n cubed EndFraction

Option a: is the equivalent expression.

Explanation:

The expression is where

Let us simplify the expression, to determine which expression is equivalent from the four options.

Multiplying the powers, we get,

Cancelling the like terms, we have,

This equation can also be written as,

Multiplying the terms in denominator, we have,

Thus, the expression which is equivalent to is

Hence, Option a is the correct answer.

first anwser choice.

step-by-step explanation:

the greater/less or equal to symbol (> or < with the line at the bottom) is a closed/filled in circle.

-5c + 2 _< _27

subtract from both sides by 2

-5c _< _ 27

divide both sides by -5

c _< _ 5.4

flip the inequality sign

c _> _5.4

the only possible answer that would match the simplified inequality is the first answer choice