What is 2x^{-3}(x^5-3x^4+x) ?

The solution to 2x^{-3}(x^5-3x^4+x) is (2(x^4-3x^3+1))/(x^2)

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simplify 2x^{-3}(x^5-3x^4+x)

simplify

2 x^{- 3} (x^{5} - 3 x^{4} + x)

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

Solution steps

2 x^{- 3} (x^{5} - 3 x^{4} + x)

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

x^{- 3} = \frac{1}{x ^{3}}

= 2 \cdot \frac{1}{x ^{3}} (x^{5} - 3 x^{4} + x)

Apply the fraction rule:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2 \cdot 1 \cdot ( x ^{5} - 3 x ^{4} + x )}{x ^{3}}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{2 ( x ^{5} - 3 x ^{4} + x )}{x ^{3}}

Factor

x^{5} - 3 x^{4} + x : x (x^{4} - 3 x^{3} + 1)

= \frac{2 x ( x ^{4} - 3 x ^{3} + 1 )}{x ^{3}}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

x^{3} = x x^{2}

= \frac{2 x ( x ^{4} - 3 x ^{3} + 1 )}{x x ^{2}}

Cancel the common factor:

x

= \frac{2 ( x ^{4} - 3 x ^{3} + 1 )}{x ^{2}}

- 3 - 4

- 7.8 - 5.6 r = 48.2

\frac{3}{4} q - 7 = 8

2 x^{2} = 3 x + 2

\frac{1}{3} s + 14 = 26

What is 2x^{-3}(x^5-3x^4+x) ?
The solution to 2x^{-3}(x^5-3x^4+x) is (2(x^4-3x^3+1))/(x^2)