Algebra Examples

$\frac{6 f^{- 2} g^{3} h^{5}}{54 f^{- 2} g^{- 5} h^{3}}$

Step 1

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

$\frac{6 f^{- 2} g^{3} h^{5} g^{5}}{54 f^{- 2} h^{3}}$

Step 2

Multiply $g^{3}$ by $g^{5}$ by adding the exponents.

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Step 2.1

Move $g^{5}$ .

$\frac{6 f^{- 2} (g^{5} g^{3}) h^{5}}{54 f^{- 2} h^{3}}$

Step 2.2

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

$\frac{6 f^{- 2} g^{5 + 3} h^{5}}{54 f^{- 2} h^{3}}$

Step 2.3

Add $5$ and $3$ .

$\frac{6 f^{- 2} g^{8} h^{5}}{54 f^{- 2} h^{3}}$

Step 3

Cancel the common factor of $6$ and $54$ .

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Step 3.1

Factor $6$ out of $6 f^{- 2} g^{8} h^{5}$ .

$\frac{6 (f^{- 2} g^{8} h^{5})}{54 f^{- 2} h^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $6$ out of $54 f^{- 2} h^{3}$ .

$\frac{6 (f^{- 2} g^{8} h^{5})}{6 (9 f^{- 2} h^{3})}$

Step 3.2.2

Cancel the common factor.

$\frac{6 (f^{- 2} g^{8} h^{5})}{6 (9 f^{- 2} h^{3})}$

Step 3.2.3

Rewrite the expression.

$\frac{f^{- 2} g^{8} h^{5}}{9 f^{- 2} h^{3}}$

Step 4

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

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Step 4.1

Cancel the common factor.

$\frac{f^{- 2} g^{8} h^{5}}{9 f^{- 2} h^{3}}$

Step 4.2

Rewrite the expression.

$\frac{g^{8} h^{5}}{9 h^{3}}$

Step 5

Cancel the common factor of $h^{5}$ and $h^{3}$ .

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Step 5.1

Factor $h^{3}$ out of $g^{8} h^{5}$ .

$\frac{h^{3} (g^{8} h^{2})}{9 h^{3}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $h^{3}$ out of $9 h^{3}$ .

$\frac{h^{3} (g^{8} h^{2})}{h^{3} \cdot 9}$

Step 5.2.2

Cancel the common factor.

$\frac{h^{3} (g^{8} h^{2})}{h^{3} \cdot 9}$

Step 5.2.3

Rewrite the expression.

$\frac{g^{8} h^{2}}{9}$