Simplify ((-6a^5b)^2)/(12a^7b)-8a^3b

$\frac{{(- 6 a^{5} b)}^{2}}{12 a^{7} b} - 8 a^{3} b$

Simplify each term.

Simplify the numerator.

Apply the product rule to $- 6 a^{5} b$ .

$\frac{{(- 6 a^{5})}^{2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Apply the product rule to $- 6 a^{5}$ .

$\frac{{(- 6)}^{2} {(a^{5})}^{2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Raise $- 6$ to the power of $2$ .

$\frac{36 {(a^{5})}^{2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

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

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

$\frac{36 a^{5 \cdot 2} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Multiply $5$ by $2$ .

$\frac{36 a^{10} b^{2}}{12 a^{7} b} - 8 a^{3} b$

Cancel the common factor of $36$ and $12$ .

Factor $12$ out of $36 a^{10} b^{2}$ .

$\frac{12 (3 a^{10} b^{2})}{12 a^{7} b} - 8 a^{3} b$

Cancel the common factors.

Factor $12$ out of $12 a^{7} b$ .

$\frac{12 (3 a^{10} b^{2})}{12 (a^{7} b)} - 8 a^{3} b$

Cancel the common factor.

$\frac{12 (3 a^{10} b^{2})}{12 (a^{7} b)} - 8 a^{3} b$

Rewrite the expression.

$\frac{3 a^{10} b^{2}}{a^{7} b} - 8 a^{3} b$

Cancel the common factor of $a^{10}$ and $a^{7}$ .

Factor $a^{7}$ out of $3 a^{10} b^{2}$ .

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} b} - 8 a^{3} b$

Cancel the common factors.

Factor $a^{7}$ out of $a^{7} b$ .

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} (b)} - 8 a^{3} b$

Cancel the common factor.

$\frac{a^{7} (3 a^{3} b^{2})}{a^{7} b} - 8 a^{3} b$

Rewrite the expression.

$\frac{3 a^{3} b^{2}}{b} - 8 a^{3} b$

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

Factor $b$ out of $3 a^{3} b^{2}$ .

$\frac{b (3 a^{3} b)}{b} - 8 a^{3} b$

Cancel the common factors.

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

$\frac{b (3 a^{3} b)}{b^{1}} - 8 a^{3} b$

Factor $b$ out of $b^{1}$ .

$\frac{b (3 a^{3} b)}{b \cdot 1} - 8 a^{3} b$

Cancel the common factor.

$\frac{b (3 a^{3} b)}{b \cdot 1} - 8 a^{3} b$

Rewrite the expression.

$\frac{3 a^{3} b}{1} - 8 a^{3} b$

Divide $3 a^{3} b$ by $1$ .

$3 a^{3} b - 8 a^{3} b$

Subtract $8 a^{3} b$ from $3 a^{3} b$ .

$- 5 a^{3} b$

Simplify ((-6a^5b)^2)/(12a^7b)-8a^3b

Related Questions

Support LCMGCF.com by disabling your adblocker.