Basic Math Examples

$\frac{{(2 A^{2} B)}^{3}}{{(2 A B^{3})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $2 A^{2} B$ .

$\frac{{(2 A^{2})}^{3} B^{3}}{{(2 A B^{3})}^{2}}$

Step 1.2

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

$\frac{2^{3} {(A^{2})}^{3} B^{3}}{{(2 A B^{3})}^{2}}$

Step 1.3

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

$\frac{8 {(A^{2})}^{3} B^{3}}{{(2 A B^{3})}^{2}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{8 A^{2 \cdot 3} B^{3}}{{(2 A B^{3})}^{2}}$

Step 1.4.2

Multiply $2$ by $3$ .

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

Step 2

Simplify the denominator.

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Step 2.1

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

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

Step 2.2

Apply the product rule to $2 A$ .

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

Step 2.3

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

$\frac{8 A^{6} B^{3}}{4 A^{2} {(B^{3})}^{2}}$

Step 2.4

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

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Step 2.4.1

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

$\frac{8 A^{6} B^{3}}{4 A^{2} B^{3 \cdot 2}}$

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{8 A^{6} B^{3}}{4 A^{2} B^{6}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $8$ and $4$ .

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Step 3.1.1

Factor $4$ out of $8 A^{6} B^{3}$ .

$\frac{4 (2 A^{6} B^{3})}{4 A^{2} B^{6}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $4 A^{2} B^{6}$ .

$\frac{4 (2 A^{6} B^{3})}{4 (A^{2} B^{6})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 (2 A^{6} B^{3})}{4 (A^{2} B^{6})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{2 A^{6} B^{3}}{A^{2} B^{6}}$

Step 3.2

Cancel the common factor of $A^{6}$ and $A^{2}$ .

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Step 3.2.1

Factor $A^{2}$ out of $2 A^{6} B^{3}$ .

$\frac{A^{2} (2 A^{4} B^{3})}{A^{2} B^{6}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $A^{2}$ out of $A^{2} B^{6}$ .

$\frac{A^{2} (2 A^{4} B^{3})}{A^{2} (B^{6})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{A^{2} (2 A^{4} B^{3})}{A^{2} B^{6}}$

Step 3.2.2.3

Rewrite the expression.

$\frac{2 A^{4} B^{3}}{B^{6}}$

Step 3.3

Cancel the common factor of $B^{3}$ and $B^{6}$ .

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Step 3.3.1

Factor $B^{3}$ out of $2 A^{4} B^{3}$ .

$\frac{B^{3} (2 A^{4})}{B^{6}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $B^{3}$ out of $B^{6}$ .

$\frac{B^{3} (2 A^{4})}{B^{3} B^{3}}$

Step 3.3.2.2

Cancel the common factor.

$\frac{B^{3} (2 A^{4})}{B^{3} B^{3}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{2 A^{4}}{B^{3}}$