Simplify 2x^4-2x^2(2x^3)^-1

$2 x^{4} \cdot - 2 x^{2} \cdot {(2 x^{3})}^{- 1}$

Step 1

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

Move $x^{2}$ .

$2 (x^{2} x^{4}) \cdot - 2 \cdot {(2 x^{3})}^{- 1}$

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

$2 x^{2 + 4} \cdot - 2 \cdot {(2 x^{3})}^{- 1}$

Add $2$ and $4$ .

$2 x^{6} \cdot - 2 \cdot {(2 x^{3})}^{- 1}$

Step 2

Multiply $- 2$ by $2$ .

$- 4 x^{6} \cdot {(2 x^{3})}^{- 1}$

Step 3

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

$- 4 x^{6} \cdot \frac{1}{2 x^{3}}$

Step 4

Cancel the common factor of $2 x^{3}$ .

Factor $2 x^{3}$ out of $- 4 x^{6}$ .

$2 x^{3} (- 2 x^{3}) \cdot \frac{1}{2 x^{3}}$

Cancel the common factor.

$2 x^{3} (- 2 x^{3}) \cdot \frac{1}{2 x^{3}}$

Rewrite the expression.

$- 2 x^{3}$

Simplify 2x^4*-2x^2*(2x^3)^-1