Simplify ((x^3)^7+x^10)/(x^4)

$\frac{{(x^{3})}^{7} + x^{10}}{x^{4}}$

Step 1

Simplify the numerator.

Multiply the exponents in ${(x^{3})}^{7}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{3 \cdot 7} + x^{10}}{x^{4}}$

Multiply $3$ by $7$ .

$\frac{x^{21} + x^{10}}{x^{4}}$

Factor $x^{10}$ out of $x^{21} + x^{10}$ .

Factor $x^{10}$ out of $x^{21}$ .

$\frac{x^{10} x^{11} + x^{10}}{x^{4}}$

Multiply by $1$ .

$\frac{x^{10} x^{11} + x^{10} \cdot 1}{x^{4}}$

Factor $x^{10}$ out of $x^{10} x^{11} + x^{10} \cdot 1$ .

$\frac{x^{10} (x^{11} + 1)}{x^{4}}$

Step 2

Simplify terms.

Cancel the common factor of $x^{10}$ and $x^{4}$ .

Factor $x^{4}$ out of $x^{10} (x^{11} + 1)$ .

$\frac{x^{4} (x^{6} (x^{11} + 1))}{x^{4}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{x^{4} (x^{6} (x^{11} + 1))}{x^{4} \cdot 1}$

Cancel the common factor.

$\frac{x^{4} (x^{6} (x^{11} + 1))}{x^{4} \cdot 1}$

Rewrite the expression.

$\frac{x^{6} (x^{11} + 1)}{1}$

Divide $x^{6} (x^{11} + 1)$ by $1$ .

$x^{6} (x^{11} + 1)$

Apply the distributive property.

$x^{6} x^{11} + x^{6} \cdot 1$

Step 3

Multiply $x^{6}$ by $x^{11}$ by adding the exponents.

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

$x^{6 + 11} + x^{6} \cdot 1$

Add $6$ and $11$ .

$x^{17} + x^{6} \cdot 1$

Step 4

Multiply $x^{6}$ by $1$ .

$x^{17} + x^{6}$