Algebra Examples

$5 x^{2} y^{3} \cdot (- 2 \frac{3}{4} x y^{6})$

Step 1

Convert $2 \frac{3}{4}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

$5 x^{2} y^{3} \cdot (- (2 + \frac{3}{4}) x y^{6})$

Step 1.2

Add $2$ and $\frac{3}{4}$ .

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Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$5 x^{2} y^{3} \cdot (- (2 \cdot \frac{4}{4} + \frac{3}{4}) x y^{6})$

Step 1.2.2

Combine $2$ and $\frac{4}{4}$ .

$5 x^{2} y^{3} \cdot (- (\frac{2 \cdot 4}{4} + \frac{3}{4}) x y^{6})$

Step 1.2.3

Combine the numerators over the common denominator.

$5 x^{2} y^{3} \cdot (- \frac{2 \cdot 4 + 3}{4} x y^{6})$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $4$ .

$5 x^{2} y^{3} \cdot (- \frac{8 + 3}{4} x y^{6})$

Step 1.2.4.2

Add $8$ and $3$ .

$5 x^{2} y^{3} \cdot (- \frac{11}{4} x y^{6})$

Step 2

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

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Step 2.1

Move $x$ .

$5 (x \cdot x^{2}) y^{3} \cdot (- \frac{11}{4} y^{6})$

Step 2.2

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

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Step 2.2.1

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

$5 (x^{1} x^{2}) y^{3} \cdot (- \frac{11}{4} y^{6})$

Step 2.2.2

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

$5 x^{1 + 2} y^{3} \cdot (- \frac{11}{4} y^{6})$

Step 2.3

Add $1$ and $2$ .

$5 x^{3} y^{3} \cdot (- \frac{11}{4} y^{6})$

Step 3

Multiply $y^{3}$ by $y^{6}$ by adding the exponents.

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Step 3.1

Move $y^{6}$ .

$5 x^{3} (y^{6} y^{3}) \cdot (- \frac{11}{4})$

Step 3.2

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

$5 x^{3} y^{6 + 3} \cdot (- \frac{11}{4})$

Step 3.3

Add $6$ and $3$ .

$5 x^{3} y^{9} \cdot (- \frac{11}{4})$

Step 4

Multiply $5 x^{3} y^{9} (- \frac{11}{4})$ .

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Step 4.1

Multiply $- 1$ by $5$ .

$- 5 x^{3} y^{9} \frac{11}{4}$

Step 4.2

Combine $- 5$ and $\frac{11}{4}$ .

$x^{3} y^{9} \frac{- 5 \cdot 11}{4}$

Step 4.3

Multiply $- 5$ by $11$ .

$x^{3} y^{9} \frac{- 55}{4}$

Step 4.4

Combine $x^{3}$ and $\frac{- 55}{4}$ .

$y^{9} \frac{x^{3} \cdot - 55}{4}$

Step 4.5

Combine $y^{9}$ and $\frac{x^{3} \cdot - 55}{4}$ .

$\frac{y^{9} (x^{3} \cdot - 55)}{4}$

Step 5

Move $- 55$ to the left of $y^{9} x^{3}$ .

$\frac{- 55 \cdot (y^{9} x^{3})}{4}$

Step 6

Move the negative in front of the fraction.

$- \frac{55 y^{9} x^{3}}{4}$