Surds and Indices Problems with Solution for Competitive Exams

Solutions of Surds and Indices Problems 

$$ Q.11.\ The \ value \ of \ (256)^{5\over4} \ is :$$

$$(A) \ 512 $$

$$ (B) \ 984 $$

$$(C) \ 1024 $$ 

$$ (D)1032 $$

$$ Q.12.\ The \ value \ of \ \left(\sqrt { 8} \  \right)^{1\over3} \ is :$$

$$(A) \ 2 $$

$$ (B) \ 4 \ $$

$$ (C) \ \sqrt { 2} \ \ $$

$$ (D) \ 8 $$

$$\left(\sqrt { 8} \  \right)^{1\over3} \ = \left(8^{{1\over2}} \right)^{1\over3}= 8^\left({1\over2}×{1\over3} \right)$$
$$ =8^{{1\over6}}=(2^3)^{1\over6}=2^\left(3×{1\over6} \right)=2^{1\over2}=\sqrt { 2} \  $$

Q.15. If 5^a = 3125, then the value of 5(a-3) is :

(A) 25                   

 (B) 125                  

(C) 625                  

(D) 1625

If 5^a = 3125 ⟺ 5^a = 5⁵ ⟺ a = 5
∴ 5^(a-3) = 5^(5-3) = 5² = 25.

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