Simplify ((12x^3y^2z)/(3x^-2y^6z^8))^-2

${(\frac{12 x^{3} y^{2} z}{3 x^{- 2} y^{6} z^{8}})}^{- 2}$

Move $x^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{12 x^{3} y^{2} z x^{2}}{3 y^{6} z^{8}})}^{- 2}$

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

${(\frac{12 (x^{2} x^{3}) y^{2} z}{3 y^{6} z^{8}})}^{- 2}$

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

${(\frac{12 x^{2 + 3} y^{2} z}{3 y^{6} z^{8}})}^{- 2}$

Add $2$ and $3$ .

${(\frac{12 x^{5} y^{2} z}{3 y^{6} z^{8}})}^{- 2}$

Cancel the common factor of $12$ and $3$ .

Factor $3$ out of $12 x^{5} y^{2} z$ .

${(\frac{3 (4 x^{5} y^{2} z)}{3 y^{6} z^{8}})}^{- 2}$

Cancel the common factors.

Factor $3$ out of $3 y^{6} z^{8}$ .

${(\frac{3 (4 x^{5} y^{2} z)}{3 (y^{6} z^{8})})}^{- 2}$

Cancel the common factor.

${(\frac{3 (4 x^{5} y^{2} z)}{3 (y^{6} z^{8})})}^{- 2}$

Rewrite the expression.

${(\frac{4 x^{5} y^{2} z}{y^{6} z^{8}})}^{- 2}$

Cancel the common factor of $y^{2}$ and $y^{6}$ .

Factor $y^{2}$ out of $4 x^{5} y^{2} z$ .

${(\frac{y^{2} (4 x^{5} z)}{y^{6} z^{8}})}^{- 2}$

Cancel the common factors.

Factor $y^{2}$ out of $y^{6} z^{8}$ .

${(\frac{y^{2} (4 x^{5} z)}{y^{2} (y^{4} z^{8})})}^{- 2}$

Cancel the common factor.

${(\frac{y^{2} (4 x^{5} z)}{y^{2} (y^{4} z^{8})})}^{- 2}$

Rewrite the expression.

${(\frac{4 x^{5} z}{y^{4} z^{8}})}^{- 2}$

Cancel the common factor of $z$ and $z^{8}$ .

Factor $z$ out of $4 x^{5} z$ .

${(\frac{z (4 x^{5})}{y^{4} z^{8}})}^{- 2}$

Cancel the common factors.

Factor $z$ out of $y^{4} z^{8}$ .

${(\frac{z (4 x^{5})}{z (y^{4} z^{7})})}^{- 2}$

Cancel the common factor.

${(\frac{z (4 x^{5})}{z (y^{4} z^{7})})}^{- 2}$

Rewrite the expression.

${(\frac{4 x^{5}}{y^{4} z^{7}})}^{- 2}$

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{y^{4} z^{7}}{4 x^{5}})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{y^{4} z^{7}}{4 x^{5}}$ .

$\frac{{(y^{4} z^{7})}^{2}}{{(4 x^{5})}^{2}}$

Apply the product rule to $y^{4} z^{7}$ .

$\frac{{(y^{4})}^{2} {(z^{7})}^{2}}{{(4 x^{5})}^{2}}$

Apply the product rule to $4 x^{5}$ .

$\frac{{(y^{4})}^{2} {(z^{7})}^{2}}{4^{2} {(x^{5})}^{2}}$

Simplify the numerator.

Multiply the exponents in ${(y^{4})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{4 \cdot 2} {(z^{7})}^{2}}{4^{2} {(x^{5})}^{2}}$

Multiply $4$ by $2$ .

$\frac{y^{8} {(z^{7})}^{2}}{4^{2} {(x^{5})}^{2}}$

Multiply the exponents in ${(z^{7})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{8} z^{7 \cdot 2}}{4^{2} {(x^{5})}^{2}}$

Multiply $7$ by $2$ .

$\frac{y^{8} z^{14}}{4^{2} {(x^{5})}^{2}}$

Simplify the denominator.

Raise $4$ to the power of $2$ .

$\frac{y^{8} z^{14}}{16 {(x^{5})}^{2}}$

Multiply the exponents in ${(x^{5})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{8} z^{14}}{16 x^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{y^{8} z^{14}}{16 x^{10}}$

Simplify ((12x^3y^2z)/(3x^-2y^6z^8))^-2

Related Questions

Support LCMGCF.com by disabling your adblocker.