Algebra Examples

$x^{5} \cdot x^{- 4} \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$

Step 1

Multiply $x^{5}$ by $x^{- 4}$ 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.

$x^{5 - 4} \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$

Step 1.2

Subtract $4$ from $5$ .

$x^{1} \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$

Step 2

Simplify $x^{1} \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$ .

$x \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$

Step 3

Multiply $x$ by $x^{10}$ by adding the exponents.

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Step 3.1

Multiply $x$ by $x^{10}$ .

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Step 3.1.1

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

$x^{1} \cdot x^{10} \cdot x^{- 3} \cdot x^{6}$

Step 3.1.2

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

$x^{1 + 10} \cdot x^{- 3} \cdot x^{6}$

Step 3.2

Add $1$ and $10$ .

$x^{11} \cdot x^{- 3} \cdot x^{6}$

Step 4

Multiply $x^{11}$ by $x^{- 3}$ 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.

$x^{11 - 3} \cdot x^{6}$

Step 4.2

Subtract $3$ from $11$ .

$x^{8} \cdot x^{6}$

Step 5

Multiply $x^{8}$ by $x^{6}$ by adding the exponents.

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Step 5.1

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

$x^{8 + 6}$

Step 5.2

Add $8$ and $6$ .

$x^{14}$