Algebra Examples

$\frac{5 {(2 a^{- 1} b^{3})}^{0}}{10 c^{- 5} d^{6} e^{- 8}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

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

$\frac{5 {(2 a^{- 1} b^{3})}^{0} c^{5}}{10 d^{6} e^{- 8}}$

Step 1.2

Move $e^{- 8}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{5 {(2 a^{- 1} b^{3})}^{0} c^{5} e^{8}}{10 d^{6}}$

Step 1.3

Cancel the common factor of $5$ and $10$ .

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Step 1.3.1

Factor $5$ out of $5 {(2 a^{- 1} b^{3})}^{0} c^{5} e^{8}$ .

$\frac{5 ({(2 a^{- 1} b^{3})}^{0} c^{5} e^{8})}{10 d^{6}}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $5$ out of $10 d^{6}$ .

$\frac{5 ({(2 a^{- 1} b^{3})}^{0} c^{5} e^{8})}{5 (2 d^{6})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{5 ({(2 a^{- 1} b^{3})}^{0} c^{5} e^{8})}{5 (2 d^{6})}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{(2 a^{- 1} b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $2 a^{- 1} b^{3}$ .

$\frac{{(2 a^{- 1})}^{0} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.2

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

$\frac{{(2 \frac{1}{a})}^{0} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.3

Combine $2$ and $\frac{1}{a}$ .

$\frac{{(\frac{2}{a})}^{0} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.4

Apply the product rule to $\frac{2}{a}$ .

$\frac{\frac{2^{0}}{a^{0}} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.5

Anything raised to $0$ is $1$ .

$\frac{\frac{1}{a^{0}} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.6

Anything raised to $0$ is $1$ .

$\frac{\frac{1}{1} {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.7

Divide $1$ by $1$ .

$\frac{1 {(b^{3})}^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.8

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

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Step 2.8.1

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

$\frac{1 b^{3 \cdot 0} c^{5} e^{8}}{2 d^{6}}$

Step 2.8.2

Multiply $3$ by $0$ .

$\frac{1 b^{0} c^{5} e^{8}}{2 d^{6}}$

Step 2.9

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 c^{5} e^{8}}{2 d^{6}}$

Step 2.10

Combine exponents.

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Step 2.10.1

Multiply $1$ by $1$ .

$\frac{1 c^{5} e^{8}}{2 d^{6}}$

Step 2.10.2

Multiply $c^{5}$ by $1$ .

$\frac{c^{5} e^{8}}{2 d^{6}}$