Pre-Algebra Examples

${(\frac{2}{3})}^{- 3}$

Step 1

Write ${(\frac{2}{3})}^{- 3}$ as an equation.

$y = {(\frac{2}{3})}^{- 3}$

Step 2

Simplify ${(\frac{2}{3})}^{- 3}$ .

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Step 2.1

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = {(\frac{3}{2})}^{3}$

Step 2.2

Apply the product rule to $\frac{3}{2}$ .

$y = \frac{3^{3}}{2^{3}}$

Step 2.3

Raise $3$ to the power of $3$ .

$y = \frac{27}{2^{3}}$

Step 2.4

Raise $2$ to the power of $3$ .

$y = \frac{27}{8}$

Step 3

The given equation $y = \frac{27}{8}$ can not be written as $y = k x^{2}$ , so $y$ doesn't vary directly with $x^{2}$ .

$y$ doesn't vary directly with $x$