What is factor e^{6x}-e^x ?

The solution to factor e^{6x}-e^x is e^x(e^x-1)(e^{4x}+e^{3x}+e^{2x}+e^x+1)

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factor e^{6x}-e^x

factor

e^{6 x} - e^{x}

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

Solution steps

e^{6 x} - e^{x}

Apply exponent rule:

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

e^{6 x} = e^{x} e^{5 x}

= e^{x} e^{5 x} - e^{x}

Factor out common term

e^{x}

= e^{x} (e^{5 x} - 1)

Factor

e^{5 x} - 1 : (e^{x} - 1) (e^{4 x} + e^{3 x} + e^{2 x} + e^{x} + 1)

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

\frac{3}{4 \frac{5}{6}}

e^{2 t} sin (h) (3 t)

0.008 a^{6} + b^{3} c^{9}

7 pq + 3 q - 49 p r - 21 r

sin (2) (2 x)

What is factor e^{6x}-e^x ?
The solution to factor e^{6x}-e^x is e^x(e^x-1)(e^{4x}+e^{3x}+e^{2x}+e^x+1)