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Verify the following rules (as we did above). Here, \( a, b \) are non-zero integers and \( m, n \) are any integers.1. Product of same powers to power of product rule: \( a^{m} \times b^{m}=(a b)^{m} \)2. Quotient of same powers to power of quotient rule: \( \frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m} \)3. Zero exponent rule: \( a^{0}=1 \). |
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Answer» (i) am x bm = [a x a x ... x a (m times)] x [b x b x ... x b (m times)] = ab x ab x ... x ab (m times) = (ab)m (ii) (a/b)m = a/b x a/b x ... x a/b (m times) \(=\frac{a\times a\times ...\times a(\text{m times})}{b\times b\times...\times b(\text{m times})}=\frac{a^m}{b^m}\) (iii) ∵ am.a-m = am x 1/am = 1 ⇒ am-m = 1 (∵ am.an = am+n) ⇒ a0 = 1 |
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