Simplify 6x*7x^-6

$6 x \cdot 7 x^{- 6}$

Step 1

Rewrite using the commutative property of multiplication.

$6 \cdot 7 x \cdot x^{- 6}$

Step 2

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

Move $x^{- 6}$ .

$6 \cdot 7 (x^{- 6} x)$

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

Raise $x$ to the power of $1$ .

$6 \cdot 7 (x^{- 6} x^{1})$

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

$6 \cdot 7 x^{- 6 + 1}$

Add $- 6$ and $1$ .

$6 \cdot 7 x^{- 5}$

Step 3

Multiply $6$ by $7$ .

$42 x^{- 5}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$42 \frac{1}{x^{5}}$

Step 5

Combine $42$ and $\frac{1}{x^{5}}$ .

$\frac{42}{x^{5}}$