Basic Math Examples

$4 n \cdot (3 n^{\frac{5}{3}}) \cdot (4 n^{\frac{4}{3}})$

Step 1

Multiply $n$ by $n^{\frac{5}{3}}$ by adding the exponents.

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Step 1.1

Move $n^{\frac{5}{3}}$ .

$4 (n^{\frac{5}{3}} n) \cdot 3 \cdot (4 n^{\frac{4}{3}})$

Step 1.2

Multiply $n^{\frac{5}{3}}$ by $n$ .

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Step 1.2.1

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

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

Step 1.2.2

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

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

Step 1.3

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

$4 n^{\frac{5}{3} + \frac{3}{3}} \cdot 3 \cdot (4 n^{\frac{4}{3}})$

Step 1.4

Combine the numerators over the common denominator.

$4 n^{\frac{5 + 3}{3}} \cdot 3 \cdot (4 n^{\frac{4}{3}})$

Step 1.5

Add $5$ and $3$ .

$4 n^{\frac{8}{3}} \cdot 3 \cdot (4 n^{\frac{4}{3}})$

Step 2

Multiply $n^{\frac{8}{3}}$ by $n^{\frac{4}{3}}$ by adding the exponents.

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Step 2.1

Move $n^{\frac{4}{3}}$ .

$4 (n^{\frac{4}{3}} n^{\frac{8}{3}}) \cdot 3 \cdot 4$

Step 2.2

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

$4 n^{\frac{4}{3} + \frac{8}{3}} \cdot 3 \cdot 4$

Step 2.3

Combine the numerators over the common denominator.

$4 n^{\frac{4 + 8}{3}} \cdot 3 \cdot 4$

Step 2.4

Add $4$ and $8$ .

$4 n^{\frac{12}{3}} \cdot 3 \cdot 4$

Step 2.5

Divide $12$ by $3$ .

$4 n^{4} \cdot 3 \cdot 4$

Step 3

Multiply $3$ by $4$ .

$12 n^{4} \cdot 4$

Step 4

Multiply $4$ by $12$ .

$48 n^{4}$