Algebra Examples

$4 y^{\frac{1}{2}} \cdot x y^{- \frac{3}{2}} \cdot 4 x^{- 2}$

Step 1

Multiply $y^{\frac{1}{2}}$ by $y^{- \frac{3}{2}}$ by adding the exponents.

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Step 1.1

Move $y^{- \frac{3}{2}}$ .

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

Step 1.2

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

$4 y^{- \frac{3}{2} + \frac{1}{2}} \cdot x \cdot (4 x^{- 2})$

Step 1.3

Combine the numerators over the common denominator.

$4 y^{\frac{- 3 + 1}{2}} \cdot x \cdot (4 x^{- 2})$

Step 1.4

Add $- 3$ and $1$ .

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

Step 1.5

Divide $- 2$ by $2$ .

$4 y^{- 1} \cdot x \cdot (4 x^{- 2})$

Step 2

Multiply $x$ by $x^{- 2}$ by adding the exponents.

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Step 2.1

Move $x^{- 2}$ .

$4 y^{- 1} \cdot (x^{- 2} x) \cdot 4$

Step 2.2

Multiply $x^{- 2}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

$4 y^{- 1} \cdot (x^{- 2} x^{1}) \cdot 4$

Step 2.2.2

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

$4 y^{- 1} \cdot x^{- 2 + 1} \cdot 4$

Step 2.3

Add $- 2$ and $1$ .

$4 y^{- 1} \cdot x^{- 1} \cdot 4$

Step 3

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

$4 \frac{1}{y} \cdot x^{- 1} \cdot 4$

Step 4

Combine $4$ and $\frac{1}{y}$ .

$\frac{4}{y} \cdot x^{- 1} \cdot 4$

Step 5

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

$\frac{4}{y} \cdot \frac{1}{x} \cdot 4$

Step 6

Multiply $\frac{4}{y}$ by $\frac{1}{x}$ .

$\frac{4}{y x} \cdot 4$

Step 7

Multiply $\frac{4}{y x} \cdot 4$ .

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Step 7.1

Combine $\frac{4}{y x}$ and $4$ .

$\frac{4 \cdot 4}{y x}$

Step 7.2

Multiply $4$ by $4$ .

$\frac{16}{y x}$