Basic Math Examples

${(36 n^{6})}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Tap for more steps...

Step 1.1

Apply the product rule to $36 n^{6}$ .

$36^{\frac{3}{2}} {(n^{6})}^{\frac{3}{2}}$

Step 1.2

Rewrite $36$ as $6^{2}$ .

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

Step 1.3

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

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

Step 2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1

Cancel the common factor.

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

Step 2.2

Rewrite the expression.

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

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Raise $6$ to the power of $3$ .

$216 {(n^{6})}^{\frac{3}{2}}$

Step 3.2

Multiply the exponents in ${(n^{6})}^{\frac{3}{2}}$ .

Tap for more steps...

Step 3.2.1

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

$216 n^{6 (\frac{3}{2})}$

Step 3.2.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1

Factor $2$ out of $6$ .

$216 n^{2 (3) \frac{3}{2}}$

Step 3.2.2.2

Cancel the common factor.

$216 n^{2 \cdot 3 \frac{3}{2}}$

Step 3.2.2.3

Rewrite the expression.

$216 n^{3 \cdot 3}$

Step 3.2.3

Multiply $3$ by $3$ .

$216 n^{9}$