Simplify (x^8y^-26)/(x^14y^-5*(x^-39y^-21))

$\frac{x^{8} y^{- 26}}{x^{14} y^{- 5} \cdot (x^{- 39} y^{- 21})}$

Step 1

Multiply $x^{14}$ by $x^{- 39}$ by adding the exponents.

Move $x^{- 39}$ .

$\frac{x^{8} y^{- 26}}{x^{- 39} x^{14} y^{- 5} \cdot y^{- 21}}$

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

$\frac{x^{8} y^{- 26}}{x^{- 39 + 14} y^{- 5} \cdot y^{- 21}}$

Add $- 39$ and $14$ .

$\frac{x^{8} y^{- 26}}{x^{- 25} y^{- 5} \cdot y^{- 21}}$

Step 2

Multiply $y^{- 5}$ by $y^{- 21}$ by adding the exponents.

Move $y^{- 21}$ .

$\frac{x^{8} y^{- 26}}{x^{- 25} (y^{- 21} y^{- 5})}$

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

$\frac{x^{8} y^{- 26}}{x^{- 25} y^{- 21 - 5}}$

Subtract $5$ from $- 21$ .

$\frac{x^{8} y^{- 26}}{x^{- 25} y^{- 26}}$

Step 3

Move $x^{- 25}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{8} y^{- 26} x^{25}}{y^{- 26}}$

Step 4

Multiply $x^{8}$ by $x^{25}$ by adding the exponents.

Move $x^{25}$ .

$\frac{x^{25} x^{8} y^{- 26}}{y^{- 26}}$

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

$\frac{x^{25 + 8} y^{- 26}}{y^{- 26}}$

Add $25$ and $8$ .

$\frac{x^{33} y^{- 26}}{y^{- 26}}$

Step 5

Cancel the common factor of $y^{- 26}$ .

Cancel the common factor.

$\frac{x^{33} y^{- 26}}{y^{- 26}}$

Divide $x^{33}$ by $1$ .

$x^{33}$