Basic Math Examples

$\frac{{(- 8 k^{3} b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $- 8 k^{3} b^{2}$ .

$\frac{{(- 8 k^{3})}^{2} {(b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.2

Apply the product rule to $- 8 k^{3}$ .

$\frac{{(- 8)}^{2} {(k^{3})}^{2} {(b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.3

Raise $- 8$ to the power of $2$ .

$\frac{64 {(k^{3})}^{2} {(b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.4

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

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Step 1.4.1

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

$\frac{64 k^{3 \cdot 2} {(b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{64 k^{6} {(b^{2})}^{2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.5

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

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Step 1.5.1

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

$\frac{64 k^{6} b^{2 \cdot 2}}{{(9 k^{5} b^{7})}^{2}}$

Step 1.5.2

Multiply $2$ by $2$ .

$\frac{64 k^{6} b^{4}}{{(9 k^{5} b^{7})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $9 k^{5} b^{7}$ .

$\frac{64 k^{6} b^{4}}{{(9 k^{5})}^{2} {(b^{7})}^{2}}$

Step 2.2

Apply the product rule to $9 k^{5}$ .

$\frac{64 k^{6} b^{4}}{9^{2} {(k^{5})}^{2} {(b^{7})}^{2}}$

Step 2.3

Raise $9$ to the power of $2$ .

$\frac{64 k^{6} b^{4}}{81 {(k^{5})}^{2} {(b^{7})}^{2}}$

Step 2.4

Multiply the exponents in ${(k^{5})}^{2}$ .

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Step 2.4.1

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

$\frac{64 k^{6} b^{4}}{81 k^{5 \cdot 2} {(b^{7})}^{2}}$

Step 2.4.2

Multiply $5$ by $2$ .

$\frac{64 k^{6} b^{4}}{81 k^{10} {(b^{7})}^{2}}$

Step 2.5

Multiply the exponents in ${(b^{7})}^{2}$ .

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Step 2.5.1

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

$\frac{64 k^{6} b^{4}}{81 k^{10} b^{7 \cdot 2}}$

Step 2.5.2

Multiply $7$ by $2$ .

$\frac{64 k^{6} b^{4}}{81 k^{10} b^{14}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $k^{6}$ and $k^{10}$ .

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Step 3.1.1

Factor $k^{6}$ out of $64 k^{6} b^{4}$ .

$\frac{k^{6} (64 b^{4})}{81 k^{10} b^{14}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $k^{6}$ out of $81 k^{10} b^{14}$ .

$\frac{k^{6} (64 b^{4})}{k^{6} (81 k^{4} b^{14})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{k^{6} (64 b^{4})}{k^{6} (81 k^{4} b^{14})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{64 b^{4}}{81 k^{4} b^{14}}$

Step 3.2

Cancel the common factor of $b^{4}$ and $b^{14}$ .

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Step 3.2.1

Factor $b^{4}$ out of $64 b^{4}$ .

$\frac{b^{4} \cdot 64}{81 k^{4} b^{14}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $b^{4}$ out of $81 k^{4} b^{14}$ .

$\frac{b^{4} \cdot 64}{b^{4} (81 k^{4} b^{10})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{b^{4} \cdot 64}{b^{4} (81 k^{4} b^{10})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{64}{81 k^{4} b^{10}}$