Basic Math Examples

${(\frac{b^{8} y^{6}}{8 b^{2} y})}^{3}$

Step 1

Cancel the common factor of $b^{8}$ and $b^{2}$ .

Tap for more steps...

Step 1.1

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

${(\frac{b^{2} (b^{6} y^{6})}{8 b^{2} y})}^{3}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $b^{2}$ out of $8 b^{2} y$ .

${(\frac{b^{2} (b^{6} y^{6})}{b^{2} (8 y)})}^{3}$

Step 1.2.2

Cancel the common factor.

${(\frac{b^{2} (b^{6} y^{6})}{b^{2} (8 y)})}^{3}$

Step 1.2.3

Rewrite the expression.

${(\frac{b^{6} y^{6}}{8 y})}^{3}$

Step 2

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

Tap for more steps...

Step 2.1

Factor $y$ out of $b^{6} y^{6}$ .

${(\frac{y (b^{6} y^{5})}{8 y})}^{3}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $y$ out of $8 y$ .

${(\frac{y (b^{6} y^{5})}{y \cdot 8})}^{3}$

Step 2.2.2

Cancel the common factor.

${(\frac{y (b^{6} y^{5})}{y \cdot 8})}^{3}$

Step 2.2.3

Rewrite the expression.

${(\frac{b^{6} y^{5}}{8})}^{3}$

Step 3

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

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{b^{6} y^{5}}{8}$ .

$\frac{{(b^{6} y^{5})}^{3}}{8^{3}}$

Step 3.2

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

$\frac{{(b^{6})}^{3} {(y^{5})}^{3}}{8^{3}}$

Step 4

Simplify the numerator.

Tap for more steps...

Step 4.1

Multiply the exponents in ${(b^{6})}^{3}$ .

Tap for more steps...

Step 4.1.1

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

$\frac{b^{6 \cdot 3} {(y^{5})}^{3}}{8^{3}}$

Step 4.1.2

Multiply $6$ by $3$ .

$\frac{b^{18} {(y^{5})}^{3}}{8^{3}}$

Step 4.2

Multiply the exponents in ${(y^{5})}^{3}$ .

Tap for more steps...

Step 4.2.1

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

$\frac{b^{18} y^{5 \cdot 3}}{8^{3}}$

Step 4.2.2

Multiply $5$ by $3$ .

$\frac{b^{18} y^{15}}{8^{3}}$

Step 5

Raise $8$ to the power of $3$ .

$\frac{b^{18} y^{15}}{512}$