Question

The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
StartFraction 1 Over 3 squared EndFraction
StartFraction 1 Over 3 cubed EndFraction
StartFraction 1 Over 9 cubed EndFraction
StartFraction 1 Over 3 Superscript 9 EndFraction

Answer 1

Answer:

B.  $\frac{1}{3^3}$

Step-by-step explanation:

We have been given an expression $3^{-3}=\frac{1}{27}$. We are asked to find an equivalent expression to $3^{-3}$.

We will use exponent properties to solve our given problem.

We will use exponent property $a^{-b}=\frac{1}{a^b}$  to rewrite our given expression.

Upon comparing our expression with exponent property, we can see that $a=3$ and $-b=-3$.

$3^{-3}=\frac{1}{3^3}$

Therefore, expression $\frac{1}{3^3}$ in equivalent to  $3^{-3}$ and option B is the correct choice.

Answer 2

Answer:

Option a: \frac{m^{5} }{162n} is the equivalent expression.

Explanation:

The expression is \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } where m\neq 0, n\neq 0

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

Multiplying the powers, we get,

\frac{3^{-3}m^{6} n^{-3}}{6mn^{-2} }

Cancelling the like terms, we have,

\frac{3^{-3}m^{5} n^{-1}}{6 }

This equation can also be written as,

\frac{m^{5}}{3^{3}6 n^{1} }

Multiplying the terms in denominator, we have,

\frac{m^{5} }{162n}

Thus, the expression which is equivalent to \frac{(3m^{-2} n)^{-3}}{6mn^{-2} } is \frac{m^{5} }{162n}

Hence, Option a is the correct answer.   23

Step-by-step explanation: