Algebra Examples

$(5 m^{\frac{4}{3}} \cdot 5 n^{\frac{1}{4}}) (m^{\frac{1}{3}} \cdot 2 n^{\frac{1}{8}})$

Step 1

Multiply $m^{\frac{4}{3}}$ by $m^{\frac{1}{3}}$ by adding the exponents.

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Step 1.1

Move $m^{\frac{1}{3}}$ .

$5 (m^{\frac{1}{3}} m^{\frac{4}{3}}) \cdot (5 n^{\frac{1}{4}}) (2 n^{\frac{1}{8}})$

Step 1.2

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

$5 m^{\frac{1}{3} + \frac{4}{3}} \cdot (5 n^{\frac{1}{4}}) (2 n^{\frac{1}{8}})$

Step 1.3

Combine the numerators over the common denominator.

$5 m^{\frac{1 + 4}{3}} \cdot (5 n^{\frac{1}{4}}) (2 n^{\frac{1}{8}})$

Step 1.4

Add $1$ and $4$ .

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1}{4}}) (2 n^{\frac{1}{8}})$

Step 2

Multiply $n^{\frac{1}{4}}$ by $n^{\frac{1}{8}}$ by adding the exponents.

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Step 2.1

Move $n^{\frac{1}{8}}$ .

$5 m^{\frac{5}{3}} \cdot (5 (n^{\frac{1}{8}} n^{\frac{1}{4}})) \cdot 2$

Step 2.2

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

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1}{8} + \frac{1}{4}}) \cdot 2$

Step 2.3

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1}{8} + \frac{1}{4} \cdot \frac{2}{2}}) \cdot 2$

Step 2.4

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.4.1

Multiply $\frac{1}{4}$ by $\frac{2}{2}$ .

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1}{8} + \frac{2}{4 \cdot 2}}) \cdot 2$

Step 2.4.2

Multiply $4$ by $2$ .

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1}{8} + \frac{2}{8}}) \cdot 2$

Step 2.5

Combine the numerators over the common denominator.

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{1 + 2}{8}}) \cdot 2$

Step 2.6

Add $1$ and $2$ .

$5 m^{\frac{5}{3}} \cdot (5 n^{\frac{3}{8}}) \cdot 2$

Step 3

Rewrite using the commutative property of multiplication.

$5 \cdot 5 m^{\frac{5}{3}} n^{\frac{3}{8}} \cdot 2$

Step 4

Multiply $5$ by $5$ .

$25 m^{\frac{5}{3}} n^{\frac{3}{8}} \cdot 2$

Step 5

Multiply $2$ by $25$ .

$50 m^{\frac{5}{3}} n^{\frac{3}{8}}$