Simplify ((10x)/(6x^4))÷((8x^2)/(3x^4))

$\frac{10 x}{6 x^{4}} \div \frac{8 x^{2}}{3 x^{4}}$

To divide by a fraction, multiply by its reciprocal.

$\frac{10 x}{6 x^{4}} \cdot \frac{3 x^{4}}{8 x^{2}}$

Combine.

$\frac{10 x (3 x^{4})}{6 x^{4} (8 x^{2})}$

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{10 (x^{4} x) \cdot 3}{6 x^{4} (8 x^{2})}$

Multiply $x^{4}$ by $x$ .

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

$\frac{10 (x^{4} x^{1}) \cdot 3}{6 x^{4} (8 x^{2})}$

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

$\frac{10 x^{4 + 1} \cdot 3}{6 x^{4} (8 x^{2})}$

Add $4$ and $1$ .

$\frac{10 x^{5} \cdot 3}{6 x^{4} (8 x^{2})}$

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{10 x^{5} \cdot 3}{6 (x^{2} x^{4}) \cdot 8}$

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

$\frac{10 x^{5} \cdot 3}{6 x^{2 + 4} \cdot 8}$

Add $2$ and $4$ .

$\frac{10 x^{5} \cdot 3}{6 x^{6} \cdot 8}$

Cancel the common factor of $10$ and $6$ .

Factor $2$ out of $10 x^{5} \cdot 3$ .

$\frac{2 (5 x^{5} \cdot 3)}{6 x^{6} \cdot 8}$

Cancel the common factors.

Factor $2$ out of $6 x^{6} \cdot 8$ .

$\frac{2 (5 x^{5} \cdot 3)}{2 (3 x^{6} \cdot 8)}$

Cancel the common factor.

$\frac{2 (5 x^{5} \cdot 3)}{2 (3 x^{6} \cdot 8)}$

Rewrite the expression.

$\frac{5 x^{5} \cdot 3}{3 x^{6} \cdot 8}$

Cancel the common factor of $x^{5}$ and $x^{6}$ .

Factor $x^{5}$ out of $5 x^{5} \cdot 3$ .

$\frac{x^{5} (5 \cdot 3)}{3 x^{6} \cdot 8}$

Cancel the common factors.

Factor $x^{5}$ out of $3 x^{6} \cdot 8$ .

$\frac{x^{5} (5 \cdot 3)}{x^{5} (3 x \cdot 8)}$

Cancel the common factor.

$\frac{x^{5} (5 \cdot 3)}{x^{5} (3 x \cdot 8)}$

Rewrite the expression.

$\frac{5 \cdot 3}{3 x \cdot 8}$

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 \cdot 3}{3 x \cdot 8}$

Rewrite the expression.

$\frac{5}{x \cdot 8}$

Move $8$ to the left of $x$ .

$\frac{5}{8 x}$

Simplify ((10x)/(6x^4))÷((8x^2)/(3x^4))

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