Simplify:$ [ ( 216 64 ) ^ 2 3 \; ( 256 81 ) ^ - 1 4 ( 16 144 ) ^ - 1 2 ]^ 1 2 $

ক) 3/4 — Laws of indices: (a m ) n = a m × n a m × a n = a m+n a m ÷ a n = a m $ [ ( 216 64 ) ^ 2/3\; ( 256 81 ) ^ - 1/4 ( 16 144 ) ^ - 1/2 ]^ 1/2 $ $= [ ( 216 64 ) ^ 2/3\; ( 81 256 ) ^ 1/4 ( 16 144 ) ^ 1/2 ]^ 1/2 ^\;$ $= [ 36 16 3 4 4 12 ]^ 1/2 \;^\; $ $= ( 9 16 )^ 1 2 ^\;$ = (3/4)

Simplify:\( [ ( 216 64 ) ^ 2 3 \; ( 256 8… | Answer

Subject

Quantitative Aptitude

Topic

Simplification

Simplify: ${\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{\frac{2}{3}\;}} \times {{\left( {\frac{{256}}{{81}}} \right)}^{ - \frac{1}{4}}} \div {{\left( {\frac{{16}}{{144}}} \right)}^{ - \frac{1}{2}}}} \right]^{\frac{1}{2}}}$
Reading

ক)

3/4

খ)

2/5

গ)

1/4

ঘ)

1/5

ঙ)

None of these

Explanation

Laws of indices: (a m ) n = a m × n a m × a n = a m+n a m ÷ a n = a m

{\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{2/3\;}} \times {{\left( {\frac{{256}}{{81}}} \right)}^{ - 1/4}} \div {{\left( {\frac{{16}}{{144}}} \right)}^{ - 1/2}}} \right]^{1/2}}

= {\left[ {{{\left( {\frac{{216}}{{64}}} \right)}^{2/3\;}} \times {{\left( {\frac{{81}}{{256}}} \right)}^{1/4}} \times {{\left( {\frac{{16}}{{144}}} \right)}^{1/2}}} \right]^{1/2}}^\; = {\left[ {\frac{{36}}{{16}} \times \frac{3}{4} \times \frac{4}{{12}}} \right]^{1/2}}{\;^\;} = {\left( {\frac{9}{{16}}} \right)^{\frac{1}{2}}}^\; = (3/4)

The difference of 1 (3/16) and its reciprocal is equal to What should come in place of question mark (?) in the following question? (43% of 2750) – (38% of 2990) =?How many (1/8)s are there in 37 (1/2)?If

x = \sqrt {\left( {1.96} \right)} - \sqrt {\left( {0.04} \right)}

then the value of x is Find the value -2+(-2)-{-(2)}-2 Let a = (4 ÷ 3) ÷ 3 ÷ 4, b = 4 ÷ (3 ÷ 3) ÷ 4, c = 4 ÷ 3 ÷ (3 ÷ 4). The maximum value among the above three is What will come in place of the question mark (?) in the following equation? 160 km 80 m ÷ 6 = ?If I = (3/4) ÷ (5/6), II = 3 ÷ [(4 ÷ 5) ÷ 6], III = [3 ÷ (4 ÷ 5)] ÷ 6, IV = 3 ÷ 4 ÷ (5 ÷ 6), then

Explanation

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