Algebra Examples

$\frac{{(8 x^{9} y^{- 7})}^{0}}{24 x^{- 3} y^{5}}$

Step 1

Move $x^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(8 x^{9} y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $8 x^{9} y^{- 7}$ .

$\frac{{(8 x^{9})}^{0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.2

Apply the product rule to $8 x^{9}$ .

$\frac{8^{0} {(x^{9})}^{0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.3

Anything raised to $0$ is $1$ .

$\frac{1 {(x^{9})}^{0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.4

Multiply ${(x^{9})}^{0}$ by $1$ .

$\frac{{(x^{9})}^{0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.5

Multiply the exponents in ${(x^{9})}^{0}$ .

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Step 2.5.1

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

$\frac{x^{9 \cdot 0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.5.2

Multiply $9$ by $0$ .

$\frac{x^{0} {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.6

Anything raised to $0$ is $1$ .

$\frac{1 {(y^{- 7})}^{0} x^{3}}{24 y^{5}}$

Step 2.7

Multiply the exponents in ${(y^{- 7})}^{0}$ .

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Step 2.7.1

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

$\frac{1 y^{- 7 \cdot 0} x^{3}}{24 y^{5}}$

Step 2.7.2

Multiply $- 7$ by $0$ .

$\frac{1 y^{0} x^{3}}{24 y^{5}}$

Step 2.8

Anything raised to $0$ is $1$ .

$\frac{1 \cdot 1 x^{3}}{24 y^{5}}$

Step 2.9

Combine exponents.

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Step 2.9.1

Multiply $1$ by $1$ .

$\frac{1 x^{3}}{24 y^{5}}$

Step 2.9.2

Multiply $x^{3}$ by $1$ .

$\frac{x^{3}}{24 y^{5}}$