Simplify 1/(2a^7)+(4-2a^3)/(a^10)

$\frac{1}{2 a^{7}} + \frac{4 - 2 a^{3}}{a^{10}}$

Factor $2$ out of $4 - 2 a^{3}$ .

Factor $2$ out of $4$ .

$\frac{1}{2 a^{7}} + \frac{2 (2) - 2 a^{3}}{a^{10}}$

Factor $2$ out of $- 2 a^{3}$ .

$\frac{1}{2 a^{7}} + \frac{2 (2) + 2 (- a^{3})}{a^{10}}$

Factor $2$ out of $2 (2) + 2 (- a^{3})$ .

$\frac{1}{2 a^{7}} + \frac{2 (2 - a^{3})}{a^{10}}$

To write $\frac{1}{2 a^{7}}$ as a fraction with a common denominator, multiply by $\frac{a^{3}}{a^{3}}$ .

$\frac{1}{2 a^{7}} \cdot \frac{a^{3}}{a^{3}} + \frac{2 (2 - a^{3})}{a^{10}}$

To write $\frac{2 (2 - a^{3})}{a^{10}}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{2 a^{7}} \cdot \frac{a^{3}}{a^{3}} + \frac{2 (2 - a^{3})}{a^{10}} \cdot \frac{2}{2}$

Write each expression with a common denominator of $2 a^{10}$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{2 a^{7}}$ by $\frac{a^{3}}{a^{3}}$ .

$\frac{a^{3}}{2 a^{7} a^{3}} + \frac{2 (2 - a^{3})}{a^{10}} \cdot \frac{2}{2}$

Multiply $a^{7}$ by $a^{3}$ by adding the exponents.

Move $a^{3}$ .

$\frac{a^{3}}{2 (a^{3} a^{7})} + \frac{2 (2 - a^{3})}{a^{10}} \cdot \frac{2}{2}$

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

$\frac{a^{3}}{2 a^{3 + 7}} + \frac{2 (2 - a^{3})}{a^{10}} \cdot \frac{2}{2}$

Add $3$ and $7$ .

$\frac{a^{3}}{2 a^{10}} + \frac{2 (2 - a^{3})}{a^{10}} \cdot \frac{2}{2}$

Multiply $\frac{2 (2 - a^{3})}{a^{10}}$ by $\frac{2}{2}$ .

$\frac{a^{3}}{2 a^{10}} + \frac{2 (2 - a^{3}) \cdot 2}{a^{10} \cdot 2}$

Reorder the factors of $a^{10} \cdot 2$ .

$\frac{a^{3}}{2 a^{10}} + \frac{2 (2 - a^{3}) \cdot 2}{2 a^{10}}$

Combine the numerators over the common denominator.

$\frac{a^{3} + 2 (2 - a^{3}) \cdot 2}{2 a^{10}}$

Simplify the numerator.

Apply the distributive property.

$\frac{a^{3} + (2 \cdot 2 + 2 (- a^{3})) \cdot 2}{2 a^{10}}$

Multiply $2$ by $2$ .

$\frac{a^{3} + (4 + 2 (- a^{3})) \cdot 2}{2 a^{10}}$

Multiply $- 1$ by $2$ .

$\frac{a^{3} + (4 - 2 a^{3}) \cdot 2}{2 a^{10}}$

Apply the distributive property.

$\frac{a^{3} + 4 \cdot 2 - 2 a^{3} \cdot 2}{2 a^{10}}$

Multiply $4$ by $2$ .

$\frac{a^{3} + 8 - 2 a^{3} \cdot 2}{2 a^{10}}$

Multiply $2$ by $- 2$ .

$\frac{a^{3} + 8 - 4 a^{3}}{2 a^{10}}$

Subtract $4 a^{3}$ from $a^{3}$ .

$\frac{- 3 a^{3} + 8}{2 a^{10}}$

Simplify with factoring out.

Factor $- 1$ out of $- 3 a^{3}$ .

$\frac{- (3 a^{3}) + 8}{2 a^{10}}$

Rewrite $8$ as $- 1 (- 8)$ .

$\frac{- (3 a^{3}) - 1 (- 8)}{2 a^{10}}$

Factor $- 1$ out of $- (3 a^{3}) - 1 (- 8)$ .

$\frac{- (3 a^{3} - 8)}{2 a^{10}}$

Simplify the expression.

Rewrite $- (3 a^{3} - 8)$ as $- 1 (3 a^{3} - 8)$ .

$\frac{- 1 (3 a^{3} - 8)}{2 a^{10}}$

Move the negative in front of the fraction.

$- \frac{3 a^{3} - 8}{2 a^{10}}$

Simplify 1/(2a^7)+(4-2a^3)/(a^10)

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