Algebra Examples

${(7 a^{3} b^{- 1})}^{0}$

Step 1

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

${(7 a^{3} \frac{1}{b})}^{0}$

Step 2

Multiply $7 a^{3} \frac{1}{b}$ .

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Step 2.1

Combine $7$ and $\frac{1}{b}$ .

${(a^{3} \frac{7}{b})}^{0}$

Step 2.2

Combine $a^{3}$ and $\frac{7}{b}$ .

${(\frac{a^{3} \cdot 7}{b})}^{0}$

Step 3

Move $7$ to the left of $a^{3}$ .

${(\frac{7 \cdot a^{3}}{b})}^{0}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{7 a^{3}}{b}$ .

$\frac{{(7 a^{3})}^{0}}{b^{0}}$

Step 4.2

Apply the product rule to $7 a^{3}$ .

$\frac{7^{0} {(a^{3})}^{0}}{b^{0}}$

Step 5

Simplify the numerator.

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Step 5.1

Anything raised to $0$ is $1$ .

$\frac{1 {(a^{3})}^{0}}{b^{0}}$

Step 5.2

Multiply the exponents in ${(a^{3})}^{0}$ .

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Step 5.2.1

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

$\frac{1 a^{3 \cdot 0}}{b^{0}}$

Step 5.2.2

Multiply $3$ by $0$ .

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

Step 5.3

Anything raised to $0$ is $1$ .

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

Step 5.4

Multiply $1$ by $1$ .

$\frac{1}{b^{0}}$

Step 6

Simplify the expression.

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Step 6.1

Anything raised to $0$ is $1$ .

$\frac{1}{1}$

Step 6.2

Divide $1$ by $1$ .

$1$