Simplify (6^7)/(6^8*6^-7)

$\frac{6^{7}}{6^{8} \cdot 6^{- 7}}$

Step 1

Multiply $6^{8}$ by $6^{- 7}$ by adding the exponents.

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

$\frac{6^{7}}{6^{8 - 7}}$

Subtract $7$ from $8$ .

$\frac{6^{7}}{6^{1}}$

Step 2

Simplify $6^{1}$ .

$\frac{6^{7}}{6}$

Step 3

Cancel the common factor of $6^{7}$ and $6$ .

Factor $6$ out of $6^{7}$ .

$\frac{6 \cdot 6^{6}}{6}$

Cancel the common factors.

Factor $6$ out of $6$ .

$\frac{6 \cdot 6^{6}}{6 (1)}$

Cancel the common factor.

$\frac{6 \cdot 6^{6}}{6 \cdot 1}$

Rewrite the expression.

$\frac{6^{6}}{1}$

Divide $6^{6}$ by $1$ .

$6^{6}$

Step 4

Raise $6$ to the power of $6$ .

$46656$