Basic Math Examples

${(\frac{2 a^{2} b}{c^{3}})}^{- 2} (3 a b^{2} c)$

Step 1

Rewrite using the commutative property of multiplication.

$3 {(\frac{2 a^{2} b}{c^{3}})}^{- 2} a b^{2} c$

Step 2

Change the sign of the exponent by rewriting the base as its reciprocal.

$3 {(\frac{c^{3}}{2 a^{2} b})}^{2} a b^{2} c$

Step 3

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

Tap for more steps...

Step 3.1

Apply the product rule to $\frac{c^{3}}{2 a^{2} b}$ .

$3 \frac{{(c^{3})}^{2}}{{(2 a^{2} b)}^{2}} a b^{2} c$

Step 3.2

Apply the product rule to $2 a^{2} b$ .

$3 \frac{{(c^{3})}^{2}}{{(2 a^{2})}^{2} b^{2}} a b^{2} c$

Step 3.3

Apply the product rule to $2 a^{2}$ .

$3 \frac{{(c^{3})}^{2}}{2^{2} {(a^{2})}^{2} b^{2}} a b^{2} c$

Step 4

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

Tap for more steps...

Step 4.1

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

$3 \frac{c^{3 \cdot 2}}{2^{2} {(a^{2})}^{2} b^{2}} a b^{2} c$

Step 4.2

Multiply $3$ by $2$ .

$3 \frac{c^{6}}{2^{2} {(a^{2})}^{2} b^{2}} a b^{2} c$

Step 5

Simplify the denominator.

Tap for more steps...

Step 5.1

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

$3 \frac{c^{6}}{4 {(a^{2})}^{2} b^{2}} a b^{2} c$

Step 5.2

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

Tap for more steps...

Step 5.2.1

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

$3 \frac{c^{6}}{4 a^{2 \cdot 2} b^{2}} a b^{2} c$

Step 5.2.2

Multiply $2$ by $2$ .

$3 \frac{c^{6}}{4 a^{4} b^{2}} a b^{2} c$

Step 6

Simplify terms.

Tap for more steps...

Step 6.1

Combine $3$ and $\frac{c^{6}}{4 a^{4} b^{2}}$ .

$\frac{3 c^{6}}{4 a^{4} b^{2}} a b^{2} c$

Step 6.2

Cancel the common factor of $a$ .

Tap for more steps...

Step 6.2.1

Factor $a$ out of $4 a^{4} b^{2}$ .

$\frac{3 c^{6}}{a (4 a^{3} b^{2})} a b^{2} c$

Step 6.2.2

Cancel the common factor.

$\frac{3 c^{6}}{a (4 a^{3} b^{2})} a b^{2} c$

Step 6.2.3

Rewrite the expression.

$\frac{3 c^{6}}{4 a^{3} b^{2}} b^{2} c$

Step 6.3

Cancel the common factor of $b^{2}$ .

Tap for more steps...

Step 6.3.1

Factor $b^{2}$ out of $4 a^{3} b^{2}$ .

$\frac{3 c^{6}}{b^{2} (4 a^{3})} b^{2} c$

Step 6.3.2

Cancel the common factor.

$\frac{3 c^{6}}{b^{2} (4 a^{3})} b^{2} c$

Step 6.3.3

Rewrite the expression.

$\frac{3 c^{6}}{4 a^{3}} c$

Step 7

Multiply $\frac{3 c^{6}}{4 a^{3}} c$ .

Tap for more steps...

Step 7.1

Combine $\frac{3 c^{6}}{4 a^{3}}$ and $c$ .

$\frac{3 c^{6} c}{4 a^{3}}$

Step 7.2

Raise $c$ to the power of $1$ .

$\frac{3 (c^{1} c^{6})}{4 a^{3}}$

Step 7.3

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

$\frac{3 c^{1 + 6}}{4 a^{3}}$

Step 7.4

Add $1$ and $6$ .

$\frac{3 c^{7}}{4 a^{3}}$