Pre-Algebra Examples

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

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

Tap for more steps...

Step 1.3.1

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

$\frac{8 p^{3 \cdot 3}}{{(3 p^{6})}^{2}}$

Step 1.3.2

Multiply $3$ by $3$ .

$\frac{8 p^{9}}{{(3 p^{6})}^{2}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Apply the product rule to $3 p^{6}$ .

$\frac{8 p^{9}}{3^{2} {(p^{6})}^{2}}$

Step 2.2

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

$\frac{8 p^{9}}{9 {(p^{6})}^{2}}$

Step 2.3

Multiply the exponents in ${(p^{6})}^{2}$ .

Tap for more steps...

Step 2.3.1

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

$\frac{8 p^{9}}{9 p^{6 \cdot 2}}$

Step 2.3.2

Multiply $6$ by $2$ .

$\frac{8 p^{9}}{9 p^{12}}$

Step 3

Cancel the common factor of $p^{9}$ and $p^{12}$ .

Tap for more steps...

Step 3.1

Factor $p^{9}$ out of $8 p^{9}$ .

$\frac{p^{9} \cdot 8}{9 p^{12}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $p^{9}$ out of $9 p^{12}$ .

$\frac{p^{9} \cdot 8}{p^{9} (9 p^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{p^{9} \cdot 8}{p^{9} (9 p^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{8}{9 p^{3}}$