How To Solve Surds And Indices Questions Quickly

Type 2: Solve Surds and Indices Quickly- Find the value of x

Question 1. If 4^x + 4^{x + 1} = 80, then the value of x^x  is

Options:

A. 16

B. 9

C. 25

D. 4

Solution:     4^x(1 + 4) = 80

4^x  * 5 = 80

4^x = \frac{80}{5}

4^x = 16

 x = 2

 x^x = 2² = 4

Correct option: D

Question 2. If 2^a = 3 \sqrt{32}, then a is equal to:

Options:

A. \frac{1}{3}

B. 4

C. \frac{5}{3}

D. \frac{1}{2}

Solution:    Given value 2^a

3 \sqrt{32}

2^a = (32)^ \frac{1}{3}

2^a = (2⁵)^ \frac{1}{3}

2^a = (2)^ \frac{5}{3}

a = \frac{5}{3}

Correct option: C

Question 3. If x and y are whole numbers such that x^y = 169, then find the value of (x – 1)^{y + 1}

Options:

A. 1331

B. 2744

C. 1728

D. 729

Solution:    169 = 13²

So, the value of x = 13 and y = 2

Now, (x – 1)^{y + 1}

= (13 – 1)²⁺¹

= (12)³ 

=1728

Correct option: C