Basic Math Examples

$\frac{- 3^{- 1} \cdot 2^{3}}{2^{- 1}}$

Step 1

Move $3^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 1 \cdot 2^{3}}{2^{- 1} \cdot 3}$

Step 2

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

$\frac{- 1 \cdot 2^{3} \cdot 2}{3}$

Step 3

Multiply $2^{3}$ by $2$ by adding the exponents.

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Step 3.1

Move $2$ .

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

Step 3.2

Multiply $2$ by $2^{3}$ .

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Step 3.2.1

Raise $2$ to the power of $1$ .

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

Step 3.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{- 1 \cdot 2^{1 + 3}}{3}$

Step 3.3

Add $1$ and $3$ .

$\frac{- 1 \cdot 2^{4}}{3}$

Step 4

Raise $2$ to the power of $4$ .

$\frac{- 1 \cdot 16}{3}$

Step 5

Multiply $- 1$ by $16$ .

$\frac{- 16}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{16}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{16}{3}$

Decimal Form:

$- 5.\overline{3}$

Mixed Number Form:

$- 5 \frac{1}{3}$