Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

One to any power is one.

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

Step 1.2

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

${(1 + 8 + 3^{3})}^{- \frac{3}{2}}$

Step 1.3

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

${(1 + 8 + 27)}^{- \frac{3}{2}}$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $1$ and $8$ .

${(9 + 27)}^{- \frac{3}{2}}$

Step 2.2

Add $9$ and $27$ .

$36^{- \frac{3}{2}}$

Step 3

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

$\frac{1}{36^{\frac{3}{2}}}$

Step 4

Simplify the denominator.

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Step 4.1

Rewrite $36$ as $6^{2}$ .

$\frac{1}{{(6^{2})}^{\frac{3}{2}}}$

Step 4.2

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

$\frac{1}{6^{2 (\frac{3}{2})}}$

Step 4.3

Cancel the common factor of $2$ .

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Step 4.3.1

Cancel the common factor.

$\frac{1}{6^{2 (\frac{3}{2})}}$

Step 4.3.2

Rewrite the expression.

$\frac{1}{6^{3}}$

Step 4.4

Raise $6$ to the power of $3$ .

$\frac{1}{216}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{216}$

Decimal Form:

$0.004\overline{629}$