Algebra Examples

$\frac{g^{0} h^{7} j^{- 2}}{g^{- 5} h^{0} j^{- 2}}$

Step 1

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

$\frac{g^{0} h^{7} j^{- 2} g^{5}}{j^{- 2}}$

Step 2

Move $h^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{g^{0} h^{7} j^{- 2} g^{5} h^{0}}{j^{- 2} h^{0}}$

Step 3

Simplify the numerator.

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Step 3.1

Multiply $g^{0}$ by $g^{5}$ by adding the exponents.

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Step 3.1.1

Move $g^{5}$ .

$\frac{g^{5} g^{0} h^{7} j^{- 2} h^{0}}{j^{- 2} h^{0}}$

Step 3.1.2

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

$\frac{g^{5 + 0} h^{7} j^{- 2} h^{0}}{j^{- 2} h^{0}}$

Step 3.1.3

Add $5$ and $0$ .

$\frac{g^{5} h^{7} j^{- 2} h^{0}}{j^{- 2} h^{0}}$

Step 3.2

Multiply $h^{7}$ by $h^{0}$ by adding the exponents.

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Step 3.2.1

Move $h^{0}$ .

$\frac{g^{5} (h^{0} h^{7}) j^{- 2}}{j^{- 2} h^{0}}$

Step 3.2.2

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

$\frac{g^{5} h^{0 + 7} j^{- 2}}{j^{- 2} h^{0}}$

Step 3.2.3

Add $0$ and $7$ .

$\frac{g^{5} h^{7} j^{- 2}}{j^{- 2} h^{0}}$

Step 4

Move $h^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{g^{5} h^{7} j^{- 2} h^{0}}{j^{- 2}}$

Step 5

Multiply $h^{7}$ by $h^{0}$ by adding the exponents.

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Step 5.1

Move $h^{0}$ .

$\frac{g^{5} (h^{0} h^{7}) j^{- 2}}{j^{- 2}}$

Step 5.2

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

$\frac{g^{5} h^{0 + 7} j^{- 2}}{j^{- 2}}$

Step 5.3

Add $0$ and $7$ .

$\frac{g^{5} h^{7} j^{- 2}}{j^{- 2}}$

Step 6

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

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Step 6.1

Cancel the common factor.

$\frac{g^{5} h^{7} j^{- 2}}{j^{- 2}}$

Step 6.2

Divide $g^{5} h^{7}$ by $1$ .

$g^{5} h^{7}$