Basic Math Examples

$a^{\frac{3}{5}} (3 a - 3)$

Step 1

Simplify by multiplying through.

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Step 1.1

Apply the distributive property.

$a^{\frac{3}{5}} (3 a) + a^{\frac{3}{5}} \cdot - 3$

Step 1.2

Reorder.

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Step 1.2.1

Rewrite using the commutative property of multiplication.

$3 a^{\frac{3}{5}} a + a^{\frac{3}{5}} \cdot - 3$

Step 1.2.2

Move $- 3$ to the left of $a^{\frac{3}{5}}$ .

$3 a^{\frac{3}{5}} a - 3 \cdot a^{\frac{3}{5}}$

Step 2

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

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Step 2.1

Move $a$ .

$3 (a \cdot a^{\frac{3}{5}}) - 3 \cdot a^{\frac{3}{5}}$

Step 2.2

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

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Step 2.2.1

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

$3 (a^{1} a^{\frac{3}{5}}) - 3 \cdot a^{\frac{3}{5}}$

Step 2.2.2

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

$3 a^{1 + \frac{3}{5}} - 3 \cdot a^{\frac{3}{5}}$

Step 2.3

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

$3 a^{\frac{5}{5} + \frac{3}{5}} - 3 \cdot a^{\frac{3}{5}}$

Step 2.4

Combine the numerators over the common denominator.

$3 a^{\frac{5 + 3}{5}} - 3 \cdot a^{\frac{3}{5}}$

Step 2.5

Add $5$ and $3$ .

$3 a^{\frac{8}{5}} - 3 \cdot a^{\frac{3}{5}}$

$3 a^{\frac{8}{5}} - 3 a^{\frac{3}{5}}$