Algebra Examples

${(\frac{2 a^{- 2}}{4 b^{2}})}^{0}$

Step 1

Move $a^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{2}{4 b^{2} a^{2}})}^{0}$

Step 2

Cancel the common factor of $2$ and $4$ .

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Step 2.1

Factor $2$ out of $2$ .

${(\frac{2 (1)}{4 b^{2} a^{2}})}^{0}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $4 b^{2} a^{2}$ .

${(\frac{2 (1)}{2 (2 b^{2} a^{2})})}^{0}$

Step 2.2.2

Cancel the common factor.

${(\frac{2 \cdot 1}{2 (2 b^{2} a^{2})})}^{0}$

Step 2.2.3

Rewrite the expression.

${(\frac{1}{2 b^{2} a^{2}})}^{0}$

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 $\frac{1}{2 b^{2} a^{2}}$ .

$\frac{1^{0}}{{(2 b^{2} a^{2})}^{0}}$

Step 3.2

Apply the product rule to $2 b^{2} a^{2}$ .

$\frac{1^{0}}{{(2 b^{2})}^{0} {(a^{2})}^{0}}$

Step 3.3

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

$\frac{1^{0}}{2^{0} {(b^{2})}^{0} {(a^{2})}^{0}}$

Step 4

Anything raised to $0$ is $1$ .

$\frac{1}{2^{0} {(b^{2})}^{0} {(a^{2})}^{0}}$

Step 5

Simplify the denominator.

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Step 5.1

Anything raised to $0$ is $1$ .

$\frac{1}{1 {(b^{2})}^{0} {(a^{2})}^{0}}$

Step 5.2

Multiply the exponents in ${(b^{2})}^{0}$ .

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Step 5.2.1

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

$\frac{1}{1 b^{2 \cdot 0} {(a^{2})}^{0}}$

Step 5.2.2

Multiply $2$ by $0$ .

$\frac{1}{1 b^{0} {(a^{2})}^{0}}$

Step 5.3

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1 {(a^{2})}^{0}}$

Step 5.4

Multiply the exponents in ${(a^{2})}^{0}$ .

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Step 5.4.1

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

$\frac{1}{1 \cdot 1 a^{2 \cdot 0}}$

Step 5.4.2

Multiply $2$ by $0$ .

$\frac{1}{1 \cdot 1 a^{0}}$

Step 5.5

Anything raised to $0$ is $1$ .

$\frac{1}{1 \cdot 1 \cdot 1}$

Step 5.6

Combine exponents.

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Step 5.6.1

Multiply $1$ by $1$ .

$\frac{1}{1 \cdot 1}$

Step 5.6.2

Multiply $1$ by $1$ .

$\frac{1}{1}$

Step 6

Divide $1$ by $1$ .

$1$