Algebra Examples

$(6 x^{3} y) {(x^{2})}^{- 2}$

Step 1

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

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Step 1.1

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

$6 x^{3} y x^{2 \cdot - 2}$

Step 1.2

Multiply $2$ by $- 2$ .

$6 x^{3} y x^{- 4}$

Step 2

Multiply $x^{3}$ by $x^{- 4}$ by adding the exponents.

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Step 2.1

Move $x^{- 4}$ .

$6 (x^{- 4} x^{3}) y$

Step 2.2

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

$6 x^{- 4 + 3} y$

Step 2.3

Add $- 4$ and $3$ .

$6 x^{- 1} y$

Step 3

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

$6 \frac{1}{x} y$

Step 4

Combine $6$ and $\frac{1}{x}$ .

$\frac{6}{x} y$

Step 5

Combine $\frac{6}{x}$ and $y$ .

$\frac{6 y}{x}$