Deloitte Surds and Indices Quiz-1

(0.04)^-1.5
=(4/100)^(-3/2)
=(1/25)^(-3/2)
=(25)^(3/2)
=5³
= 125

17^x = 4913

=>17^x = 17³

=>x=3

Now, 2^2x-1= 2^(2x3-1)= 2^6-1= 2⁵= 32

(19)^4.5 x (19)^? = 19⁹

=>(19)^(4.5+?) =(19)⁹

=>4.5+? = 9

=>? = 9 -4.5 =4.5

x^z = y²

=> 10^(0.48z) = 10^{(2 x 0.70)} = 10^1.40

=> 0.48z = 1.40

=>z= 140/48 = 2.9 (approx.)

\left (\left (\sqrt{\frac{16}{25}} \right )^{4x-9}\right )^3=\frac{64}{125}

=> \left (\left (\sqrt{\frac{16}{25}} \right )^{4x-9}\right )^3=\left ( \frac{4}{5} \right )^3

=> \left (\sqrt{\frac{16}{25}} \right )^{4x-9}= \frac{4}{5}

=> \left (\frac{4}{5} \right )^{4x-9}= \frac{4}{5}

=>4x - 9 =1

=>4x = 10

=>x = 10/4 = 5/2

36 × 36 × 36 × 36

=6² × 6² × 6² × 6²

= 6^(2+2+2+2)

= 6⁸

Let, (25)^7.5 x (5)^2.5 ÷ (125)^1.5 = 5^x

=>(5²)^7.5 x (5)^2.5 ÷ (5³)^1.5 = 5^x

=>(5)¹⁵ x (5)^2.5 ÷ (5)^4.5 = 5^x

=>(5)^(15+2.5-4.5) = 5^x

=> x = 17.5 - 4.5 = 13

5^a = 3125

=>5^a = 5⁵

=>a = 5

So, 5^{(a - 3)} = 5^{(5 - 3)} = 5² = 25

\left (\frac{a}{b} \right )^{3x-7}= \left (\frac{b}{a} \right )^{x+2}

=>\left (\frac{a}{b} \right )^{3x-7}= \left (\frac{a}{b} \right )^{(-x-2)}

=>3x-7=-x-2

=>4x = 5

=> x = 5/4

3^(x - y) = 27

=>3^(x - y)= 3^3

=> x - y = 3 ................(i)

3^(x + y) = 243

=>3^(x + y) = 3^5

=>x+y = 5 ...................(ii)

Solving, (i) and (ii) we get

x= 4