Algebra Examples

${(\frac{x^{6} \cdot x^{10}}{x^{- 3}})}^{2}$

Step 1

Multiply $x^{6}$ by $x^{10}$ 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.

${(\frac{x^{6 + 10}}{x^{- 3}})}^{2}$

Step 1.2

Add $6$ and $10$ .

${(\frac{x^{16}}{x^{- 3}})}^{2}$

Step 2

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(x^{16} x^{3})}^{2}$

Step 3

Multiply $x^{16}$ by $x^{3}$ 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.

${(x^{16 + 3})}^{2}$

Step 3.2

Add $16$ and $3$ .

${(x^{19})}^{2}$

Step 4

Multiply the exponents in ${(x^{19})}^{2}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{19 \cdot 2}$

Step 4.2

Multiply $19$ by $2$ .

$x^{38}$