Algebra Examples

${(4 (f g^{3}))}^{- 2} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(4 f g^{3})}^{2}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 f g^{3}$ .

$\frac{1}{{(4 f)}^{2} {(g^{3})}^{2}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 2.2

Apply the product rule to $4 f$ .

$\frac{1}{4^{2} f^{2} {(g^{3})}^{2}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 2.3

Raise $4$ to the power of $2$ .

$\frac{1}{16 f^{2} {(g^{3})}^{2}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 2.4

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

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Step 2.4.1

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

$\frac{1}{16 f^{2} g^{3 \cdot 2}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 2.4.2

Multiply $3$ by $2$ .

$\frac{1}{16 f^{2} g^{6}} {(- 4 f g^{3} h)}^{2} {(3 g h^{4})}^{- 1}$

Step 3

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

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Step 3.1

Apply the product rule to $- 4 f g^{3} h$ .

$\frac{1}{16 f^{2} g^{6}} ({(- 4 f g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 3.2

Apply the product rule to $- 4 f g^{3}$ .

$\frac{1}{16 f^{2} g^{6}} ({(- 4 f)}^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 3.3

Apply the product rule to $- 4 f$ .

$\frac{1}{16 f^{2} g^{6}} ({(- 4)}^{2} f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 4

Simplify the expression.

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Step 4.1

Rewrite using the commutative property of multiplication.

${(- 4)}^{2} \frac{1}{16 f^{2} g^{6}} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 4.2

Raise $- 4$ to the power of $2$ .

$16 \frac{1}{16 f^{2} g^{6}} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 5

Cancel the common factor of $16$ .

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Step 5.1

Factor $16$ out of $16 f^{2} g^{6}$ .

$16 \frac{1}{16 (f^{2} g^{6})} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 5.2

Cancel the common factor.

$16 \frac{1}{16 (f^{2} g^{6})} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 5.3

Rewrite the expression.

$\frac{1}{f^{2} g^{6}} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 6

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

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Step 6.1

Factor $f^{2}$ out of $f^{2} g^{6}$ .

$\frac{1}{f^{2} (g^{6})} (f^{2} {(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 6.2

Factor $f^{2}$ out of $f^{2} {(g^{3})}^{2} h^{2}$ .

$\frac{1}{f^{2} (g^{6})} (f^{2} ({(g^{3})}^{2} h^{2})) {(3 g h^{4})}^{- 1}$

Step 6.3

Cancel the common factor.

$\frac{1}{f^{2} g^{6}} (f^{2} ({(g^{3})}^{2} h^{2})) {(3 g h^{4})}^{- 1}$

Step 6.4

Rewrite the expression.

$\frac{1}{g^{6}} ({(g^{3})}^{2} h^{2}) {(3 g h^{4})}^{- 1}$

Step 7

Combine ${(g^{3})}^{2}$ and $\frac{1}{g^{6}}$ .

$\frac{{(g^{3})}^{2}}{g^{6}} h^{2} {(3 g h^{4})}^{- 1}$

Step 8

Combine $\frac{{(g^{3})}^{2}}{g^{6}}$ and $h^{2}$ .

$\frac{{(g^{3})}^{2} h^{2}}{g^{6}} {(3 g h^{4})}^{- 1}$

Step 9

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

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Step 9.1

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

$\frac{g^{3 \cdot 2} h^{2}}{g^{6}} {(3 g h^{4})}^{- 1}$

Step 9.2

Multiply $3$ by $2$ .

$\frac{g^{6} h^{2}}{g^{6}} {(3 g h^{4})}^{- 1}$

Step 10

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

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Step 10.1

Cancel the common factor.

$\frac{g^{6} h^{2}}{g^{6}} {(3 g h^{4})}^{- 1}$

Step 10.2

Divide $h^{2}$ by $1$ .

$h^{2} {(3 g h^{4})}^{- 1}$

Step 11

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$h^{2} \frac{1}{3 g h^{4}}$

Step 12

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

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Step 12.1

Factor $h^{2}$ out of $3 g h^{4}$ .

$h^{2} \frac{1}{h^{2} (3 g h^{2})}$

Step 12.2

Cancel the common factor.

$h^{2} \frac{1}{h^{2} (3 g h^{2})}$

Step 12.3

Rewrite the expression.

$\frac{1}{3 g h^{2}}$