Basic Math Examples

$- {(- 1000 y^{3})}^{- \frac{2}{3}}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{1}{{(- 1000 y^{3})}^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $- 1000 y^{3}$ .

$- \frac{1}{{(- 1000)}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 2.2

Rewrite $- 1000$ as ${(- 10)}^{3}$ .

$- \frac{1}{{({(- 10)}^{3})}^{\frac{2}{3}} {(y^{3})}^{\frac{2}{3}}}$

Step 2.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{1}{{(- 10)}^{3 (\frac{2}{3})} {(y^{3})}^{\frac{2}{3}}}$

Step 2.4

Cancel the common factor of $3$ .

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Step 2.4.1

Cancel the common factor.

$- \frac{1}{{(- 10)}^{3 (\frac{2}{3})} {(y^{3})}^{\frac{2}{3}}}$

Step 2.4.2

Rewrite the expression.

$- \frac{1}{{(- 10)}^{2} {(y^{3})}^{\frac{2}{3}}}$

Step 2.5

Raise $- 10$ to the power of $2$ .

$- \frac{1}{100 {(y^{3})}^{\frac{2}{3}}}$

Step 2.6

Multiply the exponents in ${(y^{3})}^{\frac{2}{3}}$ .

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Step 2.6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- \frac{1}{100 y^{3 (\frac{2}{3})}}$

Step 2.6.2

Cancel the common factor of $3$ .

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Step 2.6.2.1

Cancel the common factor.

$- \frac{1}{100 y^{3 (\frac{2}{3})}}$

Step 2.6.2.2

Rewrite the expression.

$- \frac{1}{100 y^{2}}$