1.

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: \( a^{0}=1 \).

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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