Basic Math Examples

$\frac{21^{- 11}}{7^{- 10} \cdot 3^{10}}$

Step 1

Simplify the expression.

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Step 1.1

Move $21^{- 11}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{7^{- 10} \cdot 3^{10} \cdot 21^{11}}$

Step 1.2

Move $7^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{7^{10}}{3^{10} \cdot 21^{11}}$

Step 1.3

Raise $7$ to the power of $10$ .

$\frac{282475249}{3^{10} \cdot 21^{11}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $3$ to the power of $10$ .

$\frac{282475249}{59049 \cdot 21^{11}}$

Step 2.2

Raise $21$ to the power of $11$ .

$\frac{282475249}{59049 \cdot 350277500542221}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $59049$ by $350277500542221$ .

$\frac{282475249}{20683536129517607829}$

Step 3.2

Cancel the common factor of $282475249$ and $20683536129517607829$ .

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Step 3.2.1

Factor $282475249$ out of $282475249$ .

$\frac{282475249 (1)}{20683536129517607829}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $282475249$ out of $20683536129517607829$ .

$\frac{282475249 \cdot 1}{282475249 \cdot 73222472421}$

Step 3.2.2.2

Cancel the common factor.

$\frac{282475249 \cdot 1}{282475249 \cdot 73222472421}$

Step 3.2.2.3

Rewrite the expression.

$\frac{1}{73222472421}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{73222472421}$

Decimal Form:

$1.36570094 \cdot 10^{- 11}$