Basic Math Examples

$\frac{4}{{(216)}^{- \frac{2}{3}}} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1

Simplify each term.

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Step 1.1

Move ${(216)}^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$4 \cdot 216^{\frac{2}{3}} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.2

Rewrite $216$ as $6^{3}$ .

$4 \cdot {(6^{3})}^{\frac{2}{3}} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.3

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

$4 \cdot 6^{3 (\frac{2}{3})} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Cancel the common factor.

$4 \cdot 6^{3 (\frac{2}{3})} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.4.2

Rewrite the expression.

$4 \cdot 6^{2} - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.5

Raise $6$ to the power of $2$ .

$4 \cdot 36 - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.6

Multiply $4$ by $36$ .

$144 - \frac{1}{{(256)}^{- \frac{3}{4}}}$

Step 1.7

Move ${(256)}^{- \frac{3}{4}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$144 - 256^{\frac{3}{4}}$

Step 1.8

Rewrite $256$ as $4^{4}$ .

$144 - {(4^{4})}^{\frac{3}{4}}$

Step 1.9

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

$144 - 4^{4 (\frac{3}{4})}$

Step 1.10

Cancel the common factor of $4$ .

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Step 1.10.1

Cancel the common factor.

$144 - 4^{4 (\frac{3}{4})}$

Step 1.10.2

Rewrite the expression.

$144 - 4^{3}$

Step 1.11

Raise $4$ to the power of $3$ .

$144 - 1 \cdot 64$

Step 1.12

Multiply $- 1$ by $64$ .

$144 - 64$

Step 2

Subtract $64$ from $144$ .

$80$