Basic Math Examples

$\frac{1}{2^{- 2} \cdot 2^{- 3} - 4^{5}}$

Step 1

Simplify the denominator.

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Step 1.1

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

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Step 1.1.1

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

$\frac{1}{2^{- 2 - 3} - 4^{5}}$

Step 1.1.2

Subtract $3$ from $- 2$ .

$\frac{1}{2^{- 5} - 4^{5}}$

Step 1.2

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

$\frac{1}{\frac{1}{2^{5}} - 4^{5}}$

Step 1.3

Raise $2$ to the power of $5$ .

$\frac{1}{\frac{1}{32} - 4^{5}}$

Step 1.4

Raise $4$ to the power of $5$ .

$\frac{1}{\frac{1}{32} - 1 \cdot 1024}$

Step 1.5

Multiply $- 1$ by $1024$ .

$\frac{1}{\frac{1}{32} - 1024}$

Step 1.6

To write $- 1024$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$\frac{1}{\frac{1}{32} - 1024 \cdot \frac{32}{32}}$

Step 1.7

Combine $- 1024$ and $\frac{32}{32}$ .

$\frac{1}{\frac{1}{32} + \frac{- 1024 \cdot 32}{32}}$

Step 1.8

Combine the numerators over the common denominator.

$\frac{1}{\frac{1 - 1024 \cdot 32}{32}}$

Step 1.9

Simplify the numerator.

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Step 1.9.1

Multiply $- 1024$ by $32$ .

$\frac{1}{\frac{1 - 32768}{32}}$

Step 1.9.2

Subtract $32768$ from $1$ .

$\frac{1}{\frac{- 32767}{32}}$

Step 1.10

Move the negative in front of the fraction.

$\frac{1}{- \frac{32767}{32}}$

Step 2

Cancel the common factor of $1$ and $- 1$ .

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Step 2.1

Rewrite $1$ as $- 1 (- 1)$ .

$\frac{- 1 (- 1)}{- \frac{32767}{32}}$

Step 2.2

Move the negative in front of the fraction.

$- \frac{1}{\frac{32767}{32}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$- (1 (\frac{32}{32767}))$

Step 4

Multiply $\frac{32}{32767}$ by $1$ .

$- \frac{32}{32767}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{32}{32767}$

Decimal Form:

$- 0.00097659 \dots$