Algebra Examples

$\frac{9}{16} p^{7} \cdot (- 1 \frac{1}{3} p^{4})$

Step 1

Convert $1 \frac{1}{3}$ to an improper fraction.

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Step 1.1

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

$\frac{9}{16} p^{7} \cdot (- (1 + \frac{1}{3}) p^{4})$

Step 1.2

Add $1$ and $\frac{1}{3}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

$\frac{9}{16} p^{7} \cdot (- (\frac{3}{3} + \frac{1}{3}) p^{4})$

Step 1.2.2

Combine the numerators over the common denominator.

$\frac{9}{16} p^{7} \cdot (- \frac{3 + 1}{3} p^{4})$

Step 1.2.3

Add $3$ and $1$ .

$\frac{9}{16} p^{7} \cdot (- \frac{4}{3} p^{4})$

Step 2

Rewrite using the commutative property of multiplication.

$\frac{9}{16} \cdot - 1 \frac{4}{3} p^{7} p^{4}$

Step 3

Multiply $p^{7}$ by $p^{4}$ by adding the exponents.

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Step 3.1

Move $p^{4}$ .

$\frac{9}{16} \cdot - 1 \frac{4}{3} (p^{4} p^{7})$

Step 3.2

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

$\frac{9}{16} \cdot - 1 \frac{4}{3} p^{4 + 7}$

Step 3.3

Add $4$ and $7$ .

$\frac{9}{16} \cdot - 1 \frac{4}{3} p^{11}$

Step 4

Multiply $\frac{9}{16} \cdot - 1$ .

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Step 4.1

Combine $\frac{9}{16}$ and $- 1$ .

$\frac{9 \cdot - 1}{16} \cdot \frac{4}{3} p^{11}$

Step 4.2

Multiply $9$ by $- 1$ .

$\frac{- 9}{16} \cdot \frac{4}{3} p^{11}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $- 9$ .

$\frac{3 (- 3)}{16} \cdot \frac{4}{3} p^{11}$

Step 5.2

Cancel the common factor.

$\frac{3 \cdot - 3}{16} \cdot \frac{4}{3} p^{11}$

Step 5.3

Rewrite the expression.

$\frac{- 3}{16} \cdot 4 p^{11}$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Factor $4$ out of $16$ .

$\frac{- 3}{4 (4)} \cdot 4 p^{11}$

Step 6.2

Cancel the common factor.

$\frac{- 3}{4 \cdot 4} \cdot 4 p^{11}$

Step 6.3

Rewrite the expression.

$\frac{- 3}{4} p^{11}$

Step 7

Move the negative in front of the fraction.

$- \frac{3}{4} p^{11}$

Step 8

Combine $p^{11}$ and $\frac{3}{4}$ .

$- \frac{p^{11} \cdot 3}{4}$

Step 9

Move $3$ to the left of $p^{11}$ .

$- \frac{3 p^{11}}{4}$