Algebra Examples

$(\frac{6^{- 2} x^{5}}{6^{- 3} x^{- 5}})$

Step 1

Remove parentheses.

$\frac{6^{- 2} x^{5}}{6^{- 3} x^{- 5}}$

Step 2

Move $6^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{6^{- 2} x^{5} \cdot 6^{3}}{x^{- 5}}$

Step 3

Move $x^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$6^{- 2} x^{5} \cdot 6^{3} x^{5}$

Step 4

Multiply $6^{- 2}$ by $6^{3}$ by adding the exponents.

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Step 4.1

Move $6^{3}$ .

$6^{3} \cdot 6^{- 2} x^{5} x^{5}$

Step 4.2

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

$6^{3 - 2} x^{5} x^{5}$

Step 4.3

Subtract $2$ from $3$ .

$6^{1} x^{5} x^{5}$

Step 5

Simplify $6^{1} x^{5}$ .

$6 x^{5} x^{5}$

Step 6

Multiply $x^{5}$ by $x^{5}$ by adding the exponents.

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Step 6.1

Move $x^{5}$ .

$6 (x^{5} x^{5})$

Step 6.2

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

$6 x^{5 + 5}$

Step 6.3

Add $5$ and $5$ .

$6 x^{10}$