Calculus Examples

$x^{\frac{8}{9}} (6 + x^{\frac{1}{9}})$

Step 1

Apply the distributive property.

$x^{\frac{8}{9}} \cdot 6 + x^{\frac{8}{9}} x^{\frac{1}{9}}$

Step 2

Move $6$ to the left of $x^{\frac{8}{9}}$ .

$6 \cdot x^{\frac{8}{9}} + x^{\frac{8}{9}} x^{\frac{1}{9}}$

Step 3

Multiply $x^{\frac{8}{9}}$ by $x^{\frac{1}{9}}$ by adding the exponents.

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Step 3.1

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

$6 \cdot x^{\frac{8}{9}} + x^{\frac{8}{9} + \frac{1}{9}}$

Step 3.2

Combine the numerators over the common denominator.

$6 \cdot x^{\frac{8}{9}} + x^{\frac{8 + 1}{9}}$

Step 3.3

Add $8$ and $1$ .

$6 \cdot x^{\frac{8}{9}} + x^{\frac{9}{9}}$

Step 3.4

Divide $9$ by $9$ .

$6 \cdot x^{\frac{8}{9}} + x^{1}$

Step 4

Simplify $x^{1}$ .

$6 x^{\frac{8}{9}} + x$