Question 6 Simplify 256-4-3-2

(256)^ ( 4^ 3/2 )=(256)^ (4)^ 3/2=(256)^ (2^2)^ 3/2 =(256)^ ( 2^2× 3/2 )=(256)^ (2^ 3) [∵ b^(a^m)^n=b^a^mn] =(2^8)^ ( 1/2^3 )=(2^8)^1/8 =2^8× 1/8=2^ 1=1/2 ...

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Standard VII

Mathematics

Integers

Question 6 Si...

Question

Question 6
Simplify $(256)^{- (4^{- \frac{3}{2}})}$

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Solution

$(256)^{- (4^{- \frac{3}{2}})} = (256)^{- (4)^{- \frac{3}{2}}} = (256)^{- (2^{2})^{- \frac{3}{2}}}$
$= (256)^{- (2^{2 \times - \frac{3}{2}})} = (256)^{- (2^{- 3})} [∵ b^{(a^{m})^{n}} = b^{a^{m n}}]$
$= (2^{8})^{- (\frac{1}{2^{3}})} = (2^{8})^{-} \frac{1}{8}$
$= 2^{8 \times - \frac{1}{8}} = 2^{- 1} = \frac{1}{2}$

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Question 6 Simplify (256)−(4−32)

(256)−(4−32)=(256)−(4)−32=(256)−(22)−32 =(256)−(22×−32)=(256)−(2−3)[∵b(am)n=bamn] =(28)−(123)=(28)−18 =28×−18=2−1=12

Question 6
Simplify $(256)^{- (4^{- \frac{3}{2}})}$