Basic Math Examples

${(\frac{2 n w^{2}}{6 n^{3} w^{5}})}^{2}$

Step 1

Cancel the common factor of $2$ and $6$ .

Tap for more steps...

Step 1.1

Factor $2$ out of $2 n w^{2}$ .

${(\frac{2 (n w^{2})}{6 n^{3} w^{5}})}^{2}$

Step 1.2

Cancel the common factors.

Tap for more steps...

Step 1.2.1

Factor $2$ out of $6 n^{3} w^{5}$ .

${(\frac{2 (n w^{2})}{2 (3 n^{3} w^{5})})}^{2}$

Step 1.2.2

Cancel the common factor.

${(\frac{2 (n w^{2})}{2 (3 n^{3} w^{5})})}^{2}$

Step 1.2.3

Rewrite the expression.

${(\frac{n w^{2}}{3 n^{3} w^{5}})}^{2}$

Step 2

Cancel the common factor of $n$ and $n^{3}$ .

Tap for more steps...

Step 2.1

Factor $n$ out of $n w^{2}$ .

${(\frac{n (w^{2})}{3 n^{3} w^{5}})}^{2}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $n$ out of $3 n^{3} w^{5}$ .

${(\frac{n (w^{2})}{n (3 n^{2} w^{5})})}^{2}$

Step 2.2.2

Cancel the common factor.

${(\frac{n w^{2}}{n (3 n^{2} w^{5})})}^{2}$

Step 2.2.3

Rewrite the expression.

${(\frac{w^{2}}{3 n^{2} w^{5}})}^{2}$

Step 3

Cancel the common factor of $w^{2}$ and $w^{5}$ .

Tap for more steps...

Step 3.1

Multiply by $1$ .

${(\frac{w^{2} \cdot 1}{3 n^{2} w^{5}})}^{2}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $w^{2}$ out of $3 n^{2} w^{5}$ .

${(\frac{w^{2} \cdot 1}{w^{2} (3 n^{2} w^{3})})}^{2}$

Step 3.2.2

Cancel the common factor.

${(\frac{w^{2} \cdot 1}{w^{2} (3 n^{2} w^{3})})}^{2}$

Step 3.2.3

Rewrite the expression.

${(\frac{1}{3 n^{2} w^{3}})}^{2}$

Step 4

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

Tap for more steps...

Step 4.1

Apply the product rule to $\frac{1}{3 n^{2} w^{3}}$ .

$\frac{1^{2}}{{(3 n^{2} w^{3})}^{2}}$

Step 4.2

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

$\frac{1^{2}}{{(3 n^{2})}^{2} {(w^{3})}^{2}}$

Step 4.3

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

$\frac{1^{2}}{3^{2} {(n^{2})}^{2} {(w^{3})}^{2}}$

Step 5

One to any power is one.

$\frac{1}{3^{2} {(n^{2})}^{2} {(w^{3})}^{2}}$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

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

$\frac{1}{9 {(n^{2})}^{2} {(w^{3})}^{2}}$

Step 6.2

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

Tap for more steps...

Step 6.2.1

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

$\frac{1}{9 n^{2 \cdot 2} {(w^{3})}^{2}}$

Step 6.2.2

Multiply $2$ by $2$ .

$\frac{1}{9 n^{4} {(w^{3})}^{2}}$

Step 6.3

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

Tap for more steps...

Step 6.3.1

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

$\frac{1}{9 n^{4} w^{3 \cdot 2}}$

Step 6.3.2

Multiply $3$ by $2$ .

$\frac{1}{9 n^{4} w^{6}}$