Calculus Examples

$- 63^{- 10} \cdot 32^{3}$

Step 1

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

$- \frac{1}{63^{10}} \cdot 32^{3}$

Step 2

Evaluate the exponents.

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Step 2.1

Raise $63$ to the power of $10$ .

$- \frac{1}{984930291881791000} \cdot 32^{3}$

Step 2.2

Raise $32$ to the power of $3$ .

$- \frac{1}{984930291881791000} \cdot 32768$

Step 3

Cancel the common factor of $8$ .

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Step 3.1

Move the leading negative in $- \frac{1}{984930291881791000}$ into the numerator.

$\frac{- 1}{984930291881791000} \cdot 32768$

Step 3.2

Factor $8$ out of $984930291881791000$ .

$\frac{- 1}{8 (123116286485223875)} \cdot 32768$

Step 3.3

Factor $8$ out of $32768$ .

$\frac{- 1}{8 \cdot 123116286485223875} \cdot (8 \cdot 4096)$

Step 3.4

Cancel the common factor.

$\frac{- 1}{8 \cdot 123116286485223875} \cdot (8 \cdot 4096)$

Step 3.5

Rewrite the expression.

$\frac{- 1}{123116286485223875} \cdot 4096$

Step 4

Combine $\frac{- 1}{123116286485223875}$ and $4096$ .

$\frac{- 1 \cdot 4096}{123116286485223875}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $- 1$ by $4096$ .

$\frac{- 4096}{123116286485223875}$

Step 5.2

Move the negative in front of the fraction.

$- \frac{4096}{123116286485223875}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{4096}{123116286485223875}$

Decimal Form:

$- 3.32693595 \cdot 10^{- 14}$