Algebra Examples

${(g^{5})}^{- 5} {(g^{6})}^{- 2}$

Step 1

Multiply the exponents in ${(g^{5})}^{- 5}$ .

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Step 1.1

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

$g^{5 \cdot - 5} {(g^{6})}^{- 2}$

Step 1.2

Multiply $5$ by $- 5$ .

$g^{- 25} {(g^{6})}^{- 2}$

Step 2

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

$\frac{1}{g^{25}} {(g^{6})}^{- 2}$

Step 3

Multiply the exponents in ${(g^{6})}^{- 2}$ .

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Step 3.1

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

$\frac{1}{g^{25}} g^{6 \cdot - 2}$

Step 3.2

Multiply $6$ by $- 2$ .

$\frac{1}{g^{25}} g^{- 12}$

Step 4

Cancel the common factor of $g^{- 12}$ .

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Step 4.1

Factor $g^{- 12}$ out of $g^{25}$ .

$\frac{1}{g^{- 12} g^{37}} g^{- 12}$

Step 4.2

Cancel the common factor.

$\frac{1}{g^{- 12} g^{37}} g^{- 12}$

Step 4.3

Rewrite the expression.

$\frac{1}{g^{37}}$