Algebra Examples

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

Step 1

Move ${(x y^{4})}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$x^{0} y^{2} {(x y^{4})}^{3}$

Step 2

Anything raised to $0$ is $1$ .

$1 y^{2} {(x y^{4})}^{3}$

Step 3

Multiply $y^{2}$ by $1$ .

$y^{2} {(x y^{4})}^{3}$

Step 4

Apply the product rule to $x y^{4}$ .

$y^{2} (x^{3} {(y^{4})}^{3})$

Step 5

Multiply the exponents in ${(y^{4})}^{3}$ .

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Step 5.1

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

$y^{2} (x^{3} y^{4 \cdot 3})$

Step 5.2

Multiply $4$ by $3$ .

$y^{2} (x^{3} y^{12})$

Step 6

Multiply $y^{2}$ by $y^{12}$ by adding the exponents.

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Step 6.1

Move $y^{12}$ .

$y^{12} y^{2} x^{3}$

Step 6.2

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

$y^{12 + 2} x^{3}$

Step 6.3

Add $12$ and $2$ .

$y^{14} x^{3}$