Algebra Examples

{(\frac{x^{- 3} y^{5}}{4^{- 3}})}^{0}

${(\frac{x^{- 3} y^{5}}{4^{- 3}})}^{0}$

Step 1

Move

x^{- 3}

$x^{- 3}$ to the denominator using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

{(\frac{y^{5}}{4^{- 3} x^{3}})}^{0}

${(\frac{y^{5}}{4^{- 3} x^{3}})}^{0}$

Step 2

Move

4^{- 3}

$4^{- 3}$ to the numerator using the negative exponent rule

\frac{1}{b^{- n}} = b^{n}

$\frac{1}{b^{- n}} = b^{n}$ .

{(\frac{y^{5} \cdot 4^{3}}{x^{3}})}^{0}

${(\frac{y^{5} \cdot 4^{3}}{x^{3}})}^{0}$

Step 3

Raise

4

$4$ to the power of

3

$3$ .

{(\frac{y^{5} \cdot 64}{x^{3}})}^{0}

${(\frac{y^{5} \cdot 64}{x^{3}})}^{0}$

Step 4

Move

64

$64$ to the left of

y^{5}

$y^{5}$ .

{(\frac{64 \cdot y^{5}}{x^{3}})}^{0}

${(\frac{64 \cdot y^{5}}{x^{3}})}^{0}$

Step 5

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 5.1

Apply the product rule to

\frac{64 y^{5}}{x^{3}}

$\frac{64 y^{5}}{x^{3}}$ .

\frac{{(64 y^{5})}^{0}}{{(x^{3})}^{0}}

$\frac{{(64 y^{5})}^{0}}{{(x^{3})}^{0}}$

Step 5.2

Apply the product rule to

64 y^{5}

$64 y^{5}$ .

\frac{64^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}

$\frac{64^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}$

\frac{64^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}

$\frac{64^{0} {(y^{5})}^{0}}{{(x^{3})}^{0}}$

Step 6

Simplify the numerator.

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Step 6.1

Anything raised to

0

$0$ is

1

$1$ .

\frac{1 {(y^{5})}^{0}}{{(x^{3})}^{0}}

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

Step 6.2

Multiply the exponents in

{(y^{5})}^{0}

${(y^{5})}^{0}$ .

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Step 6.2.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{1 y^{5 \cdot 0}}{{(x^{3})}^{0}}

$\frac{1 y^{5 \cdot 0}}{{(x^{3})}^{0}}$

Step 6.2.2

Multiply

5

$5$ by

0

$0$ .

\frac{1 y^{0}}{{(x^{3})}^{0}}

$\frac{1 y^{0}}{{(x^{3})}^{0}}$

\frac{1 y^{0}}{{(x^{3})}^{0}}

$\frac{1 y^{0}}{{(x^{3})}^{0}}$

Step 6.3

Anything raised to

0

$0$ is

1

$1$ .

\frac{1 \cdot 1}{{(x^{3})}^{0}}

$\frac{1 \cdot 1}{{(x^{3})}^{0}}$

Step 6.4

Multiply

1

$1$ by

1

$1$ .

\frac{1}{{(x^{3})}^{0}}

$\frac{1}{{(x^{3})}^{0}}$

\frac{1}{{(x^{3})}^{0}}

$\frac{1}{{(x^{3})}^{0}}$

Step 7

Simplify the denominator.

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Step 7.1

Multiply the exponents in

{(x^{3})}^{0}

${(x^{3})}^{0}$ .

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Step 7.1.1

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

\frac{1}{x^{3 \cdot 0}}

$\frac{1}{x^{3 \cdot 0}}$

Step 7.1.2

Multiply

3

$3$ by

0

$0$ .

\frac{1}{x^{0}}

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

\frac{1}{x^{0}}

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

Step 7.2

Anything raised to

0

$0$ is

1

$1$ .

\frac{1}{1}

$\frac{1}{1}$

\frac{1}{1}

$\frac{1}{1}$

Step 8

Divide

1

$1$ by

1

$1$ .

1

$1$