Basic Math Examples

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 ({(37 w^{8} g^{3})}^{2})}{3 d^{2} h^{6}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $37 w^{8} g^{3}$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 {(37 w^{8})}^{2} {(g^{3})}^{2}}{3 d^{2} h^{6}}$

Step 1.2

Apply the product rule to $37 w^{8}$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (37^{2} {(w^{8})}^{2}) {(g^{3})}^{2}}{3 d^{2} h^{6}}$

Step 1.3

Raise $37$ to the power of $2$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (1369 {(w^{8})}^{2}) {(g^{3})}^{2}}{3 d^{2} h^{6}}$

Step 1.4

Multiply the exponents in ${(w^{8})}^{2}$ .

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Step 1.4.1

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

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (1369 w^{8 \cdot 2}) {(g^{3})}^{2}}{3 d^{2} h^{6}}$

Step 1.4.2

Multiply $8$ by $2$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (1369 w^{16}) {(g^{3})}^{2}}{3 d^{2} h^{6}}$

Step 1.5

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

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Step 1.5.1

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

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (1369 w^{16}) g^{3 \cdot 2}}{3 d^{2} h^{6}}$

Step 1.5.2

Multiply $3$ by $2$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 (1369 w^{16}) g^{6}}{3 d^{2} h^{6}}$

${(2 p^{4} g^{7})}^{2} \cdot \frac{6 \cdot 1369 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 1.6

Multiply $6$ by $1369$ .

${(2 p^{4} g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 2

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

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Step 2.1

Apply the product rule to $2 p^{4} g^{7}$ .

${(2 p^{4})}^{2} {(g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 2.2

Apply the product rule to $2 p^{4}$ .

$2^{2} {(p^{4})}^{2} {(g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 3

Simplify the expression.

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Step 3.1

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

$4 {(p^{4})}^{2} {(g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 3.2

Multiply the exponents in ${(p^{4})}^{2}$ .

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Step 3.2.1

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

$4 p^{4 \cdot 2} {(g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 3.2.2

Multiply $4$ by $2$ .

$4 p^{8} {(g^{7})}^{2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 3.3

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

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Step 3.3.1

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

$4 p^{8} g^{7 \cdot 2} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 3.3.2

Multiply $7$ by $2$ .

$4 p^{8} g^{14} \cdot \frac{8214 w^{16} g^{6}}{3 d^{2} h^{6}}$

Step 4

Cancel the common factor of $8214$ and $3$ .

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Step 4.1

Factor $3$ out of $8214 w^{16} g^{6}$ .

$4 p^{8} g^{14} \cdot \frac{3 (2738 w^{16} g^{6})}{3 d^{2} h^{6}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3 d^{2} h^{6}$ .

$4 p^{8} g^{14} \cdot \frac{3 (2738 w^{16} g^{6})}{3 (d^{2} h^{6})}$

Step 4.2.2

Cancel the common factor.

$4 p^{8} g^{14} \cdot \frac{3 (2738 w^{16} g^{6})}{3 (d^{2} h^{6})}$

Step 4.2.3

Rewrite the expression.

$4 p^{8} g^{14} \cdot \frac{2738 w^{16} g^{6}}{d^{2} h^{6}}$

Step 5

Multiply $4 p^{8} g^{14} \frac{2738 w^{16} g^{6}}{d^{2} h^{6}}$ .

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Step 5.1

Combine $4$ and $\frac{2738 w^{16} g^{6}}{d^{2} h^{6}}$ .

$p^{8} g^{14} \frac{4 (2738 w^{16} g^{6})}{d^{2} h^{6}}$

Step 5.2

Multiply $2738$ by $4$ .

$p^{8} g^{14} \frac{10952 (w^{16} g^{6})}{d^{2} h^{6}}$

Step 5.3

Combine $p^{8}$ and $\frac{10952 (w^{16} g^{6})}{d^{2} h^{6}}$ .

$g^{14} \frac{p^{8} (10952 (w^{16} g^{6}))}{d^{2} h^{6}}$

Step 5.4

Combine $g^{14}$ and $\frac{p^{8} (10952 (w^{16} g^{6}))}{d^{2} h^{6}}$ .

$\frac{g^{14} (p^{8} (10952 (w^{16} g^{6})))}{d^{2} h^{6}}$

Step 5.5

Multiply $g^{14}$ by $g^{6}$ by adding the exponents.

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Step 5.5.1

Move $g^{6}$ .

$\frac{g^{6} g^{14} (p^{8} (10952 (w^{16})))}{d^{2} h^{6}}$

Step 5.5.2

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

$\frac{g^{6 + 14} (p^{8} (10952 (w^{16})))}{d^{2} h^{6}}$

Step 5.5.3

Add $6$ and $14$ .

$\frac{g^{20} (p^{8} (10952 (w^{16})))}{d^{2} h^{6}}$

Step 6

Move $10952$ to the left of $g^{20} p^{8}$ .

$\frac{10952 g^{20} p^{8} w^{16}}{d^{2} h^{6}}$