Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

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

Step 2

Anything raised to $0$ is $1$ .

$2 {(2 \cdot 1 y^{2})}^{- 3} y x^{3}$

Step 3

Multiply $2$ by $1$ .

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

Step 4

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

$2 \frac{1}{{(2 y^{2})}^{3}} y x^{3}$

Step 5

Simplify the denominator.

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Step 5.1

Apply the product rule to $2 y^{2}$ .

$2 \frac{1}{2^{3} {(y^{2})}^{3}} y x^{3}$

Step 5.2

Raise $2$ to the power of $3$ .

$2 \frac{1}{8 {(y^{2})}^{3}} y x^{3}$

Step 5.3

Multiply the exponents in ${(y^{2})}^{3}$ .

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Step 5.3.1

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

$2 \frac{1}{8 y^{2 \cdot 3}} y x^{3}$

Step 5.3.2

Multiply $2$ by $3$ .

$2 \frac{1}{8 y^{6}} y x^{3}$

Step 6

Simplify terms.

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Step 6.1

Cancel the common factor of $2$ .

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Step 6.1.1

Factor $2$ out of $8 y^{6}$ .

$2 \frac{1}{2 (4 y^{6})} y x^{3}$

Step 6.1.2

Cancel the common factor.

$2 \frac{1}{2 (4 y^{6})} y x^{3}$

Step 6.1.3

Rewrite the expression.

$\frac{1}{4 y^{6}} y x^{3}$

Step 6.2

Cancel the common factor of $y$ .

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Step 6.2.1

Factor $y$ out of $4 y^{6}$ .

$\frac{1}{y (4 y^{5})} y x^{3}$

Step 6.2.2

Cancel the common factor.

$\frac{1}{y (4 y^{5})} y x^{3}$

Step 6.2.3

Rewrite the expression.

$\frac{1}{4 y^{5}} x^{3}$

Step 6.3

Combine $\frac{1}{4 y^{5}}$ and $x^{3}$ .

$\frac{x^{3}}{4 y^{5}}$