Basic Math Examples

$\frac{{(6^{0} g^{4})}^{5}}{{(2 g^{2})}^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Apply the product rule to $6^{0} g^{4}$ .

$\frac{{(6^{0})}^{5} {(g^{4})}^{5}}{{(2 g^{2})}^{2}}$

Step 1.2

Multiply the exponents in ${(6^{0})}^{5}$ .

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Step 1.2.1

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

$\frac{6^{0 \cdot 5} {(g^{4})}^{5}}{{(2 g^{2})}^{2}}$

Step 1.2.2

Multiply $0$ by $5$ .

$\frac{6^{0} {(g^{4})}^{5}}{{(2 g^{2})}^{2}}$

Step 1.3

Anything raised to $0$ is $1$ .

$\frac{1 {(g^{4})}^{5}}{{(2 g^{2})}^{2}}$

Step 1.4

Multiply the exponents in ${(g^{4})}^{5}$ .

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Step 1.4.1

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

$\frac{1 g^{4 \cdot 5}}{{(2 g^{2})}^{2}}$

Step 1.4.2

Multiply $4$ by $5$ .

$\frac{1 g^{20}}{{(2 g^{2})}^{2}}$

Step 1.5

Multiply $g^{20}$ by $1$ .

$\frac{g^{20}}{{(2 g^{2})}^{2}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{g^{20}}{2^{2} {(g^{2})}^{2}}$

Step 2.2

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

$\frac{g^{20}}{4 {(g^{2})}^{2}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{g^{20}}{4 g^{2 \cdot 2}}$

Step 2.3.2

Multiply $2$ by $2$ .

$\frac{g^{20}}{4 g^{4}}$

Step 3

Cancel the common factor of $g^{20}$ and $g^{4}$ .

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Step 3.1

Factor $g^{4}$ out of $g^{20}$ .

$\frac{g^{4} g^{16}}{4 g^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $g^{4}$ out of $4 g^{4}$ .

$\frac{g^{4} g^{16}}{g^{4} \cdot 4}$

Step 3.2.2

Cancel the common factor.

$\frac{g^{4} g^{16}}{g^{4} \cdot 4}$

Step 3.2.3

Rewrite the expression.

$\frac{g^{16}}{4}$