Basic Math Examples

$\frac{4 {(a^{2} b)}^{3} \cdot (3 a^{- 5} b^{- 2})}{6 a b}$

Step 1

Move $a^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{4 {(a^{2} b)}^{3} \cdot (3 b^{- 2})}{6 a b a^{5}}$

Step 2

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

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 a b a^{5} b^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Multiply $a$ by $a^{5}$ by adding the exponents.

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Step 3.1.1

Move $a^{5}$ .

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 (a^{5} a) b \cdot b^{2}}$

Step 3.1.2

Multiply $a^{5}$ by $a$ .

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Step 3.1.2.1

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

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 (a^{5} a^{1}) b \cdot b^{2}}$

Step 3.1.2.2

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

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 a^{5 + 1} b \cdot b^{2}}$

Step 3.1.3

Add $5$ and $1$ .

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

Step 3.2

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 3.2.1

Move $b^{2}$ .

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

Step 3.2.2

Multiply $b^{2}$ by $b$ .

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Step 3.2.2.1

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

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 a^{6} (b^{2} b^{1})}$

Step 3.2.2.2

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

$\frac{4 {(a^{2} b)}^{3} \cdot 3}{6 a^{6} b^{2 + 1}}$

Step 3.2.3

Add $2$ and $1$ .

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

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $4$ and $6$ .

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Step 4.1.1

Factor $2$ out of $4 {(a^{2} b)}^{3} \cdot 3$ .

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

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $2$ out of $6 a^{6} b^{3}$ .

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

Step 4.1.2.2

Cancel the common factor.

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

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

Cancel the common factor of $3$ .

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Step 4.2.1

Cancel the common factor.

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

Step 4.2.2

Rewrite the expression.

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

Step 5

Simplify the numerator.

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Step 5.1

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

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

Step 5.2

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

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Step 5.2.1

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

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

Step 5.2.2

Multiply $2$ by $3$ .

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

Step 6

Reduce the expression by cancelling the common factors.

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Step 6.1

Cancel the common factor of $a^{6}$ .

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Step 6.1.1

Cancel the common factor.

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

Step 6.1.2

Rewrite the expression.

$\frac{2 b^{3}}{b^{3}}$

Step 6.2

Cancel the common factor of $b^{3}$ .

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Step 6.2.1

Cancel the common factor.

$\frac{2 b^{3}}{b^{3}}$

Step 6.2.2

Divide $2$ by $1$ .

$2$