Question

Answer 1

a. x²⁵ = x⁰

<=> x²⁵ = 1

<=> x = 1

b. x²⁸ = x⁵

<=> x²⁸ : x⁵ = x⁵ : x⁵

<=> x²³ = 1

<=> x = 1

c. x⁶⁴ = x

<=> x⁶⁴ : x = x : x

<=> x⁶³ = 1

<=> x = 1

Answer 2

a) \(x^{25}=x^0\)

⇒\(x^{25}=1\)

⇒\(x^{25}=1^{25}\)

⇒\(x=1\)

b) \(x^{28}=x^5\)

\(x^{28}-x^5=0\)

\(x^5\left(x^{23}-1\right)=0\)

⇔\(\left[{}\begin{matrix}x^5=0\\x^{23}-1=0\end{matrix}\right.\)

⇔\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

c) \(x^{64}=x\)

\(x^{64}-x=0\)

\(x\left(x^{63}-1\right)=0\)

⇔\(\left[{}\begin{matrix}x=0\\x^{63}-1=0\end{matrix}\right.\)

⇔\(\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)