vereinfachen 8/(sqrt((x^3+x^2+1)^3))

Lösung

vereinfachen

\frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

\frac{8}{x ^{3} + x ^{2} + 1 ( x ^{3} + x ^{2} + 1 )}

Schritte zur Lösung

\frac{8}{( x ^{3} + x ^{2} + 1 ) ^{3}}

Wende Exponentenregel an:

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

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

= \frac{8}{( x ^{3} + x ^{2} + 1 ) ^{2} ( x ^{3} + x ^{2} + 1 )}

Wende Radikal Regel an:

ab = a b,

angenommen

a \geq 0, b \geq 0

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

= \frac{8}{( x ^{3} + x ^{2} + 1 ) ^{2} x ^{3} + x ^{2} + 1}

Wende Radikal Regel an:

a^{2} = a,

angenommen

a \geq 0

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

= \frac{8}{( x ^{3} + x ^{2} + 1 ) x ^{3} + x ^{2} + 1}

= \frac{8}{x ^{3} + x ^{2} + 1 ( x ^{3} + x ^{2} + 1 )}