What is x^{-2}*(sqrt(x)+sqrt(x^7)) ?

The solution to x^{-2}*(sqrt(x)+sqrt(x^7)) is ((x+1)(x^2-x+1))/(xsqrt(x))

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simplify x^{-2}*(sqrt(x)+sqrt(x^7))

simplify

x^{- 2} \cdot (x + x^{7})

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

Solution steps

x^{- 2} (x + x^{7})

Apply exponent rule:

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

x^{- 2} = \frac{1}{x ^{2}}

= \frac{1}{x ^{2}} (x + x^{7})

Simplify

x^{7} : x^{3} x

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

Apply the fraction rule:

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

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

Apply rule:

1 \cdot a = a

1 \cdot (x + x^{3} x) = (x + x^{3} x)

= \frac{x + x ^{3} x}{x ^{2}}

Factor

x + x^{3} x : x (x + 1) (x^{2} - x + 1)

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

Apply radical rule:

a = a^{\frac{1}{2}}

x = x^{\frac{1}{2}}

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

Simplify

\frac{x ^{\frac{1}{2}}}{x ^{2}} : \frac{1}{x x}

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

\frac{( x + 3 )}{( 15 - x ^{2} - 64 )}

(3 y + 2 y)^{2}

25 x^{4} - 10 4^{2} + 16

(\frac{( 2 a ^{2} )}{( 3 b ^{2} )})^{- 2}

\frac{8 x ^{2} - 4 x y}{8 x y}

What is x^{-2}*(sqrt(x)+sqrt(x^7)) ?
The solution to x^{-2}*(sqrt(x)+sqrt(x^7)) is ((x+1)(x^2-x+1))/(xsqrt(x))