Basic Math Examples

${(\frac{{(- 3 a y^{2})}^{3} (a^{2} y)}{{(3 a^{2})}^{2} y^{5}})}^{3}$

Step 1

Cancel the common factor of $y$ and $y^{5}$ .

Tap for more steps...

Step 1.1

Factor $y$ out of ${(- 3 a y^{2})}^{3} (a^{2} y)$ .

${(\frac{y ({(- 3 a y^{2})}^{3} (a^{2}))}{{(3 a^{2})}^{2} y^{5}})}^{3}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $y$ out of ${(3 a^{2})}^{2} y^{5}$ .

${(\frac{y ({(- 3 a y^{2})}^{3} (a^{2}))}{y ({(3 a^{2})}^{2} y^{4})})}^{3}$

Step 1.2.2

Cancel the common factor.

${(\frac{y ({(- 3 a y^{2})}^{3} (a^{2}))}{y ({(3 a^{2})}^{2} y^{4})})}^{3}$

Step 1.2.3

Rewrite the expression.

${(\frac{{(- 3 a y^{2})}^{3} (a^{2})}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the product rule to $- 3 a y^{2}$ .

${(\frac{{(- 3 a)}^{3} {(y^{2})}^{3} a^{2}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.2

Apply the product rule to $- 3 a$ .

${(\frac{{(- 3)}^{3} a^{3} {(y^{2})}^{3} a^{2}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.3

Raise $- 3$ to the power of $3$ .

${(\frac{- 27 a^{3} {(y^{2})}^{3} a^{2}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.4

Multiply the exponents in ${(y^{2})}^{3}$ .

Tap for more steps...

Step 2.4.1

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

${(\frac{- 27 a^{3} y^{2 \cdot 3} a^{2}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.4.2

Multiply $2$ by $3$ .

${(\frac{- 27 a^{3} y^{6} a^{2}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.5

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

Tap for more steps...

Step 2.5.1

Move $a^{2}$ .

${(\frac{- 27 (a^{2} a^{3}) y^{6}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.5.2

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

${(\frac{- 27 a^{2 + 3} y^{6}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 2.5.3

Add $2$ and $3$ .

${(\frac{- 27 a^{5} y^{6}}{{(3 a^{2})}^{2} y^{4}})}^{3}$

Step 3

Simplify the denominator.

Tap for more steps...

Step 3.1

Apply the product rule to $3 a^{2}$ .

${(\frac{- 27 a^{5} y^{6}}{3^{2} {(a^{2})}^{2} y^{4}})}^{3}$

Step 3.2

Raise $3$ to the power of $2$ .

${(\frac{- 27 a^{5} y^{6}}{9 {(a^{2})}^{2} y^{4}})}^{3}$

Step 3.3

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

Tap for more steps...

Step 3.3.1

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

${(\frac{- 27 a^{5} y^{6}}{9 a^{2 \cdot 2} y^{4}})}^{3}$

Step 3.3.2

Multiply $2$ by $2$ .

${(\frac{- 27 a^{5} y^{6}}{9 a^{4} y^{4}})}^{3}$

Step 4

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 4.1

Cancel the common factor of $- 27$ and $9$ .

Tap for more steps...

Step 4.1.1

Factor $9$ out of $- 27 a^{5} y^{6}$ .

${(\frac{9 (- 3 a^{5} y^{6})}{9 a^{4} y^{4}})}^{3}$

Step 4.1.2

Cancel the common factors.

Tap for more steps...

Step 4.1.2.1

Factor $9$ out of $9 a^{4} y^{4}$ .

${(\frac{9 (- 3 a^{5} y^{6})}{9 (a^{4} y^{4})})}^{3}$

Step 4.1.2.2

Cancel the common factor.

${(\frac{9 (- 3 a^{5} y^{6})}{9 (a^{4} y^{4})})}^{3}$

Step 4.1.2.3

Rewrite the expression.

${(\frac{- 3 a^{5} y^{6}}{a^{4} y^{4}})}^{3}$

Step 4.2

Cancel the common factor of $a^{5}$ and $a^{4}$ .

Tap for more steps...

Step 4.2.1

Factor $a^{4}$ out of $- 3 a^{5} y^{6}$ .

${(\frac{a^{4} (- 3 a y^{6})}{a^{4} y^{4}})}^{3}$

Step 4.2.2

Cancel the common factors.

Tap for more steps...

Step 4.2.2.1

Factor $a^{4}$ out of $a^{4} y^{4}$ .

${(\frac{a^{4} (- 3 a y^{6})}{a^{4} (y^{4})})}^{3}$

Step 4.2.2.2

Cancel the common factor.

${(\frac{a^{4} (- 3 a y^{6})}{a^{4} y^{4}})}^{3}$

Step 4.2.2.3

Rewrite the expression.

${(\frac{- 3 a y^{6}}{y^{4}})}^{3}$

Step 4.3

Cancel the common factor of $y^{6}$ and $y^{4}$ .

Tap for more steps...

Step 4.3.1

Factor $y^{4}$ out of $- 3 a y^{6}$ .

${(\frac{y^{4} (- 3 a y^{2})}{y^{4}})}^{3}$

Step 4.3.2

Cancel the common factors.

Tap for more steps...

Step 4.3.2.1

Multiply by $1$ .

${(\frac{y^{4} (- 3 a y^{2})}{y^{4} \cdot 1})}^{3}$

Step 4.3.2.2

Cancel the common factor.

${(\frac{y^{4} (- 3 a y^{2})}{y^{4} \cdot 1})}^{3}$

Step 4.3.2.3

Rewrite the expression.

${(\frac{- 3 a y^{2}}{1})}^{3}$

Step 4.3.2.4

Divide $- 3 a y^{2}$ by $1$ .

${(- 3 a y^{2})}^{3}$

Step 5

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

Tap for more steps...

Step 5.1

Apply the product rule to $- 3 a y^{2}$ .

${(- 3 a)}^{3} {(y^{2})}^{3}$

Step 5.2

Apply the product rule to $- 3 a$ .

${(- 3)}^{3} a^{3} {(y^{2})}^{3}$

Step 6

Raise $- 3$ to the power of $3$ .

$- 27 a^{3} {(y^{2})}^{3}$

Step 7

Multiply the exponents in ${(y^{2})}^{3}$ .

Tap for more steps...

Step 7.1

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

$- 27 a^{3} y^{2 \cdot 3}$

Step 7.2

Multiply $2$ by $3$ .

$- 27 a^{3} y^{6}$