Evaluate- i5-32 - 5-32 ii5-66 - 5-6-4 iii2-3-3- 2-3-2 iv9-8-3- 9-82

(i)(5/3)^2 × (5/3)^2 =(5/3)^2+2=(5/3)^4 =5/3×5/3×5/3×5/3=625/81 (ii)(5/6)^6 × (5/6)^ 4=(5/6)^6 4=(5/6)^2 =5/6×5/6=25/36 (iii)(2/3)^ 3× (2/3)^ 2=(3/2)^3 × (3/2) ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with like Bases

Evaluate: i5/...

Question

Evaluate:

$(i) (\frac{5}{3})^{2} \times (\frac{5}{3})^{2}$

$(i i) (\frac{5}{6})^{6} \times (\frac{5}{6})^{- 4}$

$(i i i) (\frac{2}{3})^{- 3} \times (\frac{2}{3})^{- 2}$

$(i v) (\frac{9}{8})^{- 3} \times (\frac{9}{8})^{2}$

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Solution

$(i) (\frac{5}{3})^{2} \times (\frac{5}{3})^{2} = (\frac{5}{3})^{2 + 2} = (\frac{5}{3})^{4}$

$= \frac{5}{3} \times \frac{5}{3} \times \frac{5}{3} \times \frac{5}{3} = \frac{625}{81}$

$(i i) (\frac{5}{6})^{6} \times (\frac{5}{6})^{- 4} = (\frac{5}{6})^{6 - 4} = (\frac{5}{6})^{2}$

$= \frac{5}{6} \times \frac{5}{6} = \frac{25}{36} (i i i) (\frac{2}{3})^{- 3} \times (\frac{2}{3})^{- 2} = (\frac{3}{2})^{3} \times (\frac{3}{2})^{2}$

$= (\frac{3}{2})^{3 + 2} = (\frac{3}{2})^{5} = \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2} \times \frac{3}{2}$

$= \frac{243}{32}$

$(i v) (\frac{9}{8})^{- 3} \times (\frac{9}{8})^{2} = (\frac{9}{8})^{- 3 + 2} = (\frac{9}{8})^{- 1}$

$= \frac{8}{9}$

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Evaluate: (i)(53)2×(53)2 (ii)(56)6×(56)−4 (iii)(23)−3×(23)−2 (iv)(98)−3×(98)2

(i)(53)2×(53)2=(53)2+2=(53)4 =53×53×53×53=62581 (ii)(56)6×(56)−4=(56)6−4=(56)2 =56×56=2536(iii)(23)−3×(23)−2=(32)3×(32)2 =(32)3+2=(32)5=32×32×32×32×32 =24332 (iv)(98)−3×(98)2=(98)−3+2=(98)−1 =89

Evaluate:

$(i) (\frac{5}{3})^{2} \times (\frac{5}{3})^{2}$

$(i i) (\frac{5}{6})^{6} \times (\frac{5}{6})^{- 4}$

$(i i i) (\frac{2}{3})^{- 3} \times (\frac{2}{3})^{- 2}$

$(i v) (\frac{9}{8})^{- 3} \times (\frac{9}{8})^{2}$