Algebra Examples

$\frac{4^{- 2} x^{3} y^{- 3}}{2 x^{0}}$

Step 1

Move $4^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{3} y^{- 3}}{2 x^{0} \cdot 4^{2}}$

Step 2

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

$\frac{x^{3}}{2 x^{0} \cdot 4^{2} y^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $4$ as $2^{2}$ .

$\frac{x^{3}}{{(2^{2})}^{2} \cdot 2 x^{0} y^{3}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{x^{3}}{2^{2 \cdot 2} \cdot 2 x^{0} y^{3}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{x^{3}}{2^{4} \cdot 2 x^{0} y^{3}}$

Step 3.3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{3}}{2^{4 + 1} x^{0} y^{3}}$

Step 3.4

Add $4$ and $1$ .

$\frac{x^{3}}{2^{5} x^{0} y^{3}}$

Step 4

Move $x^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{3} x^{0}}{2^{5} y^{3}}$

Step 5

Multiply $x^{3}$ by $x^{0}$ by adding the exponents.

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Step 5.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{3 + 0}}{2^{5} y^{3}}$

Step 5.2

Add $3$ and $0$ .

$\frac{x^{3}}{2^{5} y^{3}}$

Step 6

Raise $2$ to the power of $5$ .

$\frac{x^{3}}{32 y^{3}}$