Basic Math Examples

$\frac{{(k^{2})}^{- 2} \cdot (p^{3}) \cdot (12 z^{4})}{p^{2} \cdot (3 k^{3}) \cdot (4 z^{3})}$

Step 1

Multiply.

Tap for more steps...

Step 1.1

Move ${(k^{2})}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{p^{3} \cdot (12 z^{4})}{p^{2} \cdot (3 k^{3}) \cdot (4 z^{3}) {(k^{2})}^{2}}$

Step 1.2

Multiply $4$ by $3$ .

$\frac{p^{3} \cdot (12 z^{4})}{p^{2} \cdot (12 k^{3}) \cdot z^{3} {(k^{2})}^{2}}$

Step 2

Cancel the common factor of $p^{3}$ and $p^{2}$ .

Tap for more steps...

Step 2.1

Factor $p^{2}$ out of $p^{3} \cdot (12 z^{4})$ .

$\frac{p^{2} (p \cdot (12 z^{4}))}{p^{2} \cdot (12 k^{3}) \cdot z^{3} {(k^{2})}^{2}}$

Step 2.2

Cancel the common factors.

Tap for more steps...

Step 2.2.1

Factor $p^{2}$ out of $p^{2} \cdot (12 k^{3}) \cdot z^{3} {(k^{2})}^{2}$ .

$\frac{p^{2} (p \cdot (12 z^{4}))}{p^{2} ((12 k^{3}) \cdot z^{3} {(k^{2})}^{2})}$

Step 2.2.2

Cancel the common factor.

$\frac{p^{2} (p \cdot (12 z^{4}))}{p^{2} ((12 k^{3}) \cdot z^{3} {(k^{2})}^{2})}$

Step 2.2.3

Rewrite the expression.

$\frac{p \cdot (12 z^{4})}{(12 k^{3}) \cdot z^{3} {(k^{2})}^{2}}$

Step 3

Cancel the common factor of $12$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

$\frac{p \cdot (12 z^{4})}{12 k^{3} \cdot z^{3} {(k^{2})}^{2}}$

Step 3.2

Rewrite the expression.

$\frac{p \cdot (z^{4})}{(k^{3}) \cdot z^{3} {(k^{2})}^{2}}$

Step 4

Cancel the common factor of $z^{4}$ and $z^{3}$ .

Tap for more steps...

Step 4.1

Factor $z^{3}$ out of $p \cdot (z^{4})$ .

$\frac{z^{3} (p \cdot (z))}{(k^{3}) \cdot z^{3} {(k^{2})}^{2}}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $z^{3}$ out of $(k^{3}) \cdot z^{3} {(k^{2})}^{2}$ .

$\frac{z^{3} (p \cdot (z))}{z^{3} ((k^{3}) {(k^{2})}^{2})}$

Step 4.2.2

Cancel the common factor.

$\frac{z^{3} (p \cdot (z))}{z^{3} ((k^{3}) {(k^{2})}^{2})}$

Step 4.2.3

Rewrite the expression.

$\frac{p \cdot (z)}{(k^{3}) {(k^{2})}^{2}}$

Step 5

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

Tap for more steps...

Step 5.1

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

$\frac{p \cdot z}{k^{3} k^{2 \cdot 2}}$

Step 5.2

Multiply $2$ by $2$ .

$\frac{p \cdot z}{k^{3} k^{4}}$

Step 6

Multiply $k^{3}$ by $k^{4}$ by adding the exponents.

Tap for more steps...

Step 6.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{p \cdot z}{k^{3 + 4}}$

Step 6.2

Add $3$ and $4$ .

$\frac{p \cdot z}{k^{7}}$

$\frac{p z}{k^{7}}$