Evaluate (52x^6)/(13x^-7)

$\frac{52 x^{6}}{13 x^{- 7}}$

Step 1

Move $x^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{52 x^{6} x^{7}}{13}$

Step 2

Multiply $x^{6}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{52 (x^{7} x^{6})}{13}$

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

$\frac{52 x^{7 + 6}}{13}$

Add $7$ and $6$ .

$\frac{52 x^{13}}{13}$

Step 3

Cancel the common factor of $52$ and $13$ .

Factor $13$ out of $52 x^{13}$ .

$\frac{13 (4 x^{13})}{13}$

Cancel the common factors.

Factor $13$ out of $13$ .

$\frac{13 (4 x^{13})}{13 (1)}$

Cancel the common factor.

$\frac{13 (4 x^{13})}{13 \cdot 1}$

Rewrite the expression.

$\frac{4 x^{13}}{1}$

Divide $4 x^{13}$ by $1$ .

$4 x^{13}$