Simplify (15q^6+5q^2)(5q^4)^-1

$(15 q^{6} + 5 q^{2}) {(5 q^{4})}^{- 1}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$(15 q^{6} + 5 q^{2}) \frac{1}{5 q^{4}}$

Step 2

Multiply $15 q^{6} + 5 q^{2}$ by $\frac{1}{5 q^{4}}$ .

$\frac{15 q^{6} + 5 q^{2}}{5 q^{4}}$

Step 3

Factor $5 q^{2}$ out of $15 q^{6} + 5 q^{2}$ .

Factor $5 q^{2}$ out of $15 q^{6}$ .

$\frac{5 q^{2} (3 q^{4}) + 5 q^{2}}{5 q^{4}}$

Factor $5 q^{2}$ out of $5 q^{2}$ .

$\frac{5 q^{2} (3 q^{4}) + 5 q^{2} (1)}{5 q^{4}}$

Factor $5 q^{2}$ out of $5 q^{2} (3 q^{4}) + 5 q^{2} (1)$ .

$\frac{5 q^{2} (3 q^{4} + 1)}{5 q^{4}}$

Step 4

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 q^{2} (3 q^{4} + 1)}{5 q^{4}}$

Rewrite the expression.

$\frac{q^{2} (3 q^{4} + 1)}{q^{4}}$

Step 5

Cancel the common factors.

Factor $q^{2}$ out of $q^{4}$ .

$\frac{q^{2} (3 q^{4} + 1)}{q^{2} q^{2}}$

Cancel the common factor.

$\frac{q^{2} (3 q^{4} + 1)}{q^{2} q^{2}}$

Rewrite the expression.

$\frac{3 q^{4} + 1}{q^{2}}$