Question

Find the value of x so that (–2)³ × (–2)^–6 = (–2)^{2x – 1}

Answer 1

We have (–2)³ × (–2)^–6 = (–2)^{2x – 1}

Using law of exponents,

a^m × aⁿ = (a)^{m + n}  ...[∵ a is non-zero integer]

Then, (–2)³ × (–2)^–6 = (–2)^{2x – 1}

⇒ (–2)^{3 – 6} = (–2)^{2x – 1}

⇒ (–2)^–3 = (–2)^{2x – 1}

On comparing both sides, we get

–3 = 2x – 1

⇒ 2x = –2

⇒ x = –1