Basic Math Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

$\frac{16 {(c^{3})}^{4} {(y^{2})}^{4}}{{(4 c y^{2})}^{2}}$

Step 1.4

Multiply the exponents in ${(c^{3})}^{4}$ .

Tap for more steps...

Step 1.4.1

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

$\frac{16 c^{3 \cdot 4} {(y^{2})}^{4}}{{(4 c y^{2})}^{2}}$

Step 1.4.2

Multiply $3$ by $4$ .

$\frac{16 c^{12} {(y^{2})}^{4}}{{(4 c y^{2})}^{2}}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

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

$\frac{16 c^{12} y^{2 \cdot 4}}{{(4 c y^{2})}^{2}}$

Step 1.5.2

Multiply $2$ by $4$ .

$\frac{16 c^{12} y^{8}}{{(4 c y^{2})}^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $4 c y^{2}$ .

$\frac{16 c^{12} y^{8}}{{(4 c)}^{2} {(y^{2})}^{2}}$

Step 2.2

Apply the product rule to $4 c$ .

$\frac{16 c^{12} y^{8}}{4^{2} c^{2} {(y^{2})}^{2}}$

Step 2.3

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

$\frac{16 c^{12} y^{8}}{16 c^{2} {(y^{2})}^{2}}$

Step 2.4

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

Tap for more steps...

Step 2.4.1

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

$\frac{16 c^{12} y^{8}}{16 c^{2} y^{2 \cdot 2}}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{16 c^{12} y^{8}}{16 c^{2} y^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Cancel the common factor of $16$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\frac{16 c^{12} y^{8}}{16 c^{2} y^{4}}$

Step 3.1.2

Rewrite the expression.

$\frac{c^{12} y^{8}}{c^{2} y^{4}}$

Step 3.2

Cancel the common factor of $c^{12}$ and $c^{2}$ .

Tap for more steps...

Step 3.2.1

Factor $c^{2}$ out of $c^{12} y^{8}$ .

$\frac{c^{2} (c^{10} y^{8})}{c^{2} y^{4}}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $c^{2}$ out of $c^{2} y^{4}$ .

$\frac{c^{2} (c^{10} y^{8})}{c^{2} (y^{4})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{c^{2} (c^{10} y^{8})}{c^{2} y^{4}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{c^{10} y^{8}}{y^{4}}$

Step 3.3

Cancel the common factor of $y^{8}$ and $y^{4}$ .

Tap for more steps...

Step 3.3.1

Factor $y^{4}$ out of $c^{10} y^{8}$ .

$\frac{y^{4} (c^{10} y^{4})}{y^{4}}$

Step 3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.1

Multiply by $1$ .

$\frac{y^{4} (c^{10} y^{4})}{y^{4} \cdot 1}$

Step 3.3.2.2

Cancel the common factor.

$\frac{y^{4} (c^{10} y^{4})}{y^{4} \cdot 1}$

Step 3.3.2.3

Rewrite the expression.

$\frac{c^{10} y^{4}}{1}$

Step 3.3.2.4

Divide $c^{10} y^{4}$ by $1$ .

$c^{10} y^{4}$