Algebra Examples

$13^{- 21} \cdot 13^{- 4} \cdot 13^{- 5} \cdot 13^{14} \cdot 13^{- 6}$

Step 1

Multiply $13^{- 21}$ by $13^{- 4}$ by adding the exponents.

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Step 1.1

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

$13^{- 21 - 4} \cdot 13^{- 5} \cdot 13^{14} \cdot 13^{- 6}$

Step 1.2

Subtract $4$ from $- 21$ .

$13^{- 25} \cdot 13^{- 5} \cdot 13^{14} \cdot 13^{- 6}$

Step 2

Multiply $13^{- 25}$ by $13^{- 5}$ by adding the exponents.

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Step 2.1

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

$13^{- 25 - 5} \cdot 13^{14} \cdot 13^{- 6}$

Step 2.2

Subtract $5$ from $- 25$ .

$13^{- 30} \cdot 13^{14} \cdot 13^{- 6}$

Step 3

Multiply $13^{- 30}$ by $13^{14}$ by adding the exponents.

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Step 3.1

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

$13^{- 30 + 14} \cdot 13^{- 6}$

Step 3.2

Add $- 30$ and $14$ .

$13^{- 16} \cdot 13^{- 6}$

Step 4

Multiply $13^{- 16}$ by $13^{- 6}$ by adding the exponents.

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Step 4.1

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

$13^{- 16 - 6}$

Step 4.2

Subtract $6$ from $- 16$ .

$13^{- 22}$

Step 5

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

$\frac{1}{13^{22}}$

Step 6

Raise $13$ to the power of $22$ .

$\frac{1}{3211838877954860000000000}$