Correct answer is option - 3
Explanation:
Applying the laws of exponents, it gives: 3^{p + 3} = 3^p * 3³ = x * 27 = 27x.

Correct answer is option - 4
Explanation:
The expression 1/i can be multiplied in the numerator and the denominator by i.
This gives: (1 * i)/ (i * i) = i/ i². In complex numbers, i² = -1.
Hence we get, i/-1 = -i.

Correct answer is option - 5
Explanation:
The given expression, (6x³)² can be written in terms of 2x³ as: (3 * 2x³)² = (3)² * (2x³)².
This gives: 9 * (8)² = 9 * 64 = 576.

Correct answer is option - 3
Explanation: Multiplying the numerator and denominator of the expression by √3, we get:
(√5 * √3)/ (√3 * √3) = √(5 * 3)/ √(3 * 3) = √15/√9 = (√15)/3.
Therefore the expression √(5/3) can also be written as (√15)/3.

Correct answer is option - 3
Explanation: Laura’s original income = $120 and new income = $150.
Increase in Laura’s income = $150 - $120 = $30.
In order to find the percentage increase in her income, we can use the formula:
% percentage increase = (increase in income * 100%) / (original income)
This gives: % percentage increase = ($30 * 100%)/ $120 = 25%.

Correct answer is option - 1
Explanation:
If | f(x) | = a, then according to the absolute value property: f(x) = a, or f(x) = -a.
Similarly the absolute value expression |x – 4| < 2 can be written as: -2 < x – 4 < 2.
Here 4 can be added to each side and this gives: (-2 + 4) < (x – 4 + 4) < (2 + 4)
This gives: 2 < x < 6.
 

Correct answer is option - 3
Explanation:
From the given figure, it can be observed that PCQ is a right angled triangle with PQ as the hypotenuse.
The length PC = CQ as tangents drawn to a circle from the same external point are equal in length.
Let the length PC = CQ = x, then by the Pythagorean Theorem we get, 2x² = 6² = 36.
This gives: x² = 18. From the figure, the length PC = radius of the circle.
Hence area of the circle = π * (radius)² = π * 18 = 18π.