Simplify (7x^3y^-4z^-6)/(84x^-7y^-1z^-4)

$\frac{7 x^{3} y^{- 4} z^{- 6}}{84 x^{- 7} y^{- 1} z^{- 4}}$

Step 1

Move $y^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{7 x^{3} z^{- 6}}{84 x^{- 7} y^{- 1} z^{- 4} y^{4}}$

Step 2

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

$\frac{7 x^{3}}{84 x^{- 7} y^{- 1} z^{- 4} y^{4} z^{6}}$

Step 3

Simplify the denominator.

Multiply $y^{- 1}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$\frac{7 x^{3}}{84 x^{- 7} (y^{4} y^{- 1}) z^{- 4} z^{6}}$

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

$\frac{7 x^{3}}{84 x^{- 7} y^{4 - 1} z^{- 4} z^{6}}$

Subtract $1$ from $4$ .

$\frac{7 x^{3}}{84 x^{- 7} y^{3} z^{- 4} z^{6}}$

Multiply $z^{- 4}$ by $z^{6}$ by adding the exponents.

Move $z^{6}$ .

$\frac{7 x^{3}}{84 x^{- 7} y^{3} (z^{6} z^{- 4})}$

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

$\frac{7 x^{3}}{84 x^{- 7} y^{3} z^{6 - 4}}$

Subtract $4$ from $6$ .

$\frac{7 x^{3}}{84 x^{- 7} y^{3} z^{2}}$

Step 4

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

$\frac{7 x^{3} x^{7}}{84 y^{3} z^{2}}$

Step 5

Multiply $x^{3}$ by $x^{7}$ by adding the exponents.

Move $x^{7}$ .

$\frac{7 (x^{7} x^{3})}{84 y^{3} z^{2}}$

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

$\frac{7 x^{7 + 3}}{84 y^{3} z^{2}}$

Add $7$ and $3$ .

$\frac{7 x^{10}}{84 y^{3} z^{2}}$

Step 6

Cancel the common factor of $7$ and $84$ .

Factor $7$ out of $7 x^{10}$ .

$\frac{7 (x^{10})}{84 y^{3} z^{2}}$

Cancel the common factors.

Factor $7$ out of $84 y^{3} z^{2}$ .

$\frac{7 (x^{10})}{7 (12 y^{3} z^{2})}$

Cancel the common factor.

$\frac{7 x^{10}}{7 (12 y^{3} z^{2})}$

Rewrite the expression.

$\frac{x^{10}}{12 y^{3} z^{2}}$