Question

Jayne evaluated an expression that has a value of StartFraction 1 Over 729 EndFraction. Which expression could Jayne have evaluated? Check all that apply.

Answer 1

Option b: $9^{-3}$

Option c: $3^{-6}$

Explanation:

The given expression is $\frac{1}{729}$

To determine from the options which are equivalent to the expression $\frac{1}{729}$

Option a: $(-9)^{3}$

Simplifying the expression, we have,

$(-9)^{3}=-9\times-9\times-9=-729$

which is not an equivalent expression to $\frac{1}{729}$

Hence, Option a is not the correct answer.

Option b: $9^{-3}$

Simplifying the expression, we have,

$9^{-3}=\frac{1}{9^{3} } =\frac{1}{729}$

which is an equivalent expression to  $\frac{1}{729}$

Hence, Option b is the correct answer.

Option c: $3^{-6}$

Simplifying the expression, we have,

$3^{-6}=\frac{1}{3^{6} } =\frac{1}{729}$

which is an equivalent expression to  $\frac{1}{729}$

Hence, Option c is the correct answer.

Option d: $\left(\frac{1}{9}\right)^{-6}$

Simplifying the expression, we have,

$\left(\frac{1}{9}\right)^{-6}=\frac{1}{\left(\frac{1}{9}\right)^{6}}=\frac{1}{\frac{1}{531441}}=531441$

which is not an equivalent expression to $\frac{1}{729}$

Hence, Option d is not the correct answer.

Option e: $\left(\frac{1}{3}\right)^{-6}$

Simplifying the expression, we have,

$\left(\frac{1}{3}\right)^{-6}=\frac{1}{\left(\frac{1}{3}\right)^{6}}=\frac{1}{\frac{1}{729}}=729$

which is not an equivalent expression to $\frac{1}{729}$

Hence, Option e is not the correct answer.

Option f: $(-3)^{6}$

Simplifying the expression, we have,

$(-3)^{6}=-3\times-3\times-3\times-3\times-3\times-3=-729$

which is not an equivalent expression to $\frac{1}{729}$

Hence, Option f is not the correct answer.

Answer 2

Answer:

I agree with the person above me

Step-by-step explanation:

(2 and 3)