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Question
Find the value of x so that (–2)3 × (–2)–6 = (–2)2x – 1
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Solution
We have (–2)3 × (–2)–6 = (–2)2x – 1
Using law of exponents,
am × 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
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