General Questions

Answer: Option D

Explanation:

4 ^{(x – y)} = 64

4 ^{(x – y)} = 64 = 43

Equation 1) x – y = 3

4 ^{(x + y)} = 1024 = 4⁵

Equation 2) x + y = 5

Solving equation (1) and (2), we get

x = 4 and y = 1

Crosscheck the answers by substituting the values of x and y in the given expression.

4 ^{(4 – 1)} = 4³ = 64 and 4 ^{(4 + 1)} = 4⁵ = 1024

Hence, the answers x = 4 and y = 1 are correct.

Answer: Option D

Explanation:

x^m × xⁿ = x^{m + n}

9^x – 9^{x – 1} = 648

9^{x –} 1 (9 – 1) = 648

9^{x – 1} = (648/8) = 81

9^{x – 1} = 9²

x – 1 = 2

x = 2 + 1 = 3

x^x = 3³ = 27

Alternate solution:

Select the given options and substitute the value of x = 5, 6, 1.5 and 3 in the given expression.

Substituting value of x = 3,

9^x – 9^{x – 1} = ?

9³ – 9^{3 – 1} = 648

Value of x = 3

x^x = 3³ = 27

Answer: Option D

Explanation:

We know that 11² = 121.

Putting m = 11 and n = 2, we get:

(m - 1)^{n + 1} = (11 - 1)^{(2 + 1)} = 10³ = 1000.

Answer: Option D

Explanation:

Let (17)^3.5 x (17)^x = 17⁸.

Then, (17)^{3.5 + x} = 17⁸.

 3.5 + x = 8

 x = (8 - 3.5)

 x = 4.5

Answer: Option B

Explanation:

Answer: Option C

Explanation:

Answer: Option C

Explanation:

Cube root of 1331 is 11. Therefore,
 (11³)^{– (2/3)}

 Hint: 
 Remember the law of indices (x^m)ⁿ = x^mn

 (11) ^{– 3 × (2/3)} = 11^–2

 Hint:  x^-1  = 1/x

11^-2  = 1/121