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Simplify: (i) 2^2/3× 2^1/5 (ii) (1/3^3)^7 (iii) 11^1/2/11^1/4 (iv) 7^1/2× 8^1/2
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24/05/2021 10:57 am
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Simplify:
(i) 2^{2/3}× 2^{1/5}
(ii) (1/3^{3})^{7}
(iii) 11^{1/2}/11^{1/4}
(iv) 7^{1/2}× 8^{1/2}
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24/05/2021 10:58 am
(i) 2^{2/3 }× 2^{1/5}
2^{2/3}×2^{1/5 }= 2^{(2/3)+(1/5)} [⸪Since, a^{m}×a^{n }= a^{m+n}____ Laws of exponents]
= 2^{13/15} [⸪ 2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]
(ii) (1/3^{3})^{7}
(1/3^{3})^{7 }= (3^{3})^{7} [⸪Since,(a^{m})^{n }= a^{m x n}____ Laws of exponents]
= 3^{21}
(iii) 11^{1/2}/11^{1/4}
11^{1/2}/11^{1/4 }= 11^{(1/2)(1/4)}
= 11^{1/4} [⸪(1/2) – (1/4) = (1×42×1)/(2×4) = 42)/8 = 2/8 = ¼ ]
(iv) 7^{1/2}×8^{1/2}
7^{1/2}×8^{1/2} = (7×8)^{1/2} [⸪Since, (a^{m}×b^{m }= (a×b)^{m} ____ Laws of exponents]
= 56^{1/2}
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