Simplify (4a^3-8a^2+a^2)(4a)^-1

$(4 a^{3} - 8 a^{2} + a^{2}) {(4 a)}^{- 1}$

Step 1

Add $- 8 a^{2}$ and $a^{2}$ .

$(4 a^{3} - 7 a^{2}) {(4 a)}^{- 1}$

Step 2

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

$(4 a^{3} - 7 a^{2}) \frac{1}{4 a}$

Step 3

Multiply $4 a^{3} - 7 a^{2}$ by $\frac{1}{4 a}$ .

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

Step 4

Factor $a^{2}$ out of $4 a^{3} - 7 a^{2}$ .

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

$\frac{a^{2} (4 a) - 7 a^{2}}{4 a}$

Factor $a^{2}$ out of $- 7 a^{2}$ .

$\frac{a^{2} (4 a) + a^{2} \cdot - 7}{4 a}$

Factor $a^{2}$ out of $a^{2} (4 a) + a^{2} \cdot - 7$ .

$\frac{a^{2} (4 a - 7)}{4 a}$

Step 5

Cancel the common factor of $a^{2}$ and $a$ .

Factor $a$ out of $a^{2} (4 a - 7)$ .

$\frac{a (a (4 a - 7))}{4 a}$

Cancel the common factors.

Factor $a$ out of $4 a$ .

$\frac{a (a (4 a - 7))}{a \cdot 4}$

Cancel the common factor.

$\frac{a (a (4 a - 7))}{a \cdot 4}$

Rewrite the expression.

$\frac{a (4 a - 7)}{4}$