# Surds and Indices Questions Solved

Surds and Indices Questions Solved contains examples of solved questions and explanations for each question’s solutions. Test yourself on Surds and Indices.

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## Surds and Indices Questions Solved

Below are the few Surds and Indices Questions Solved:

### Question 1

#### Solution 1

As per the law of multiplication of indices:

am x an = am+n

On substituting values : a = 139, m = 7, n = x and (m+n) = 10

m + n = (m+n) => 7 + x = 10
=> x = 10 – 7
x = 3.

### Question 2

#### Solution 2

As per the law of the division of indices:

am / an = am-n

On substituting values : a = 81, m = 7, n = x and (m-n) = 5

m – n = (m – n) => 7 – x = 5
=> -x = 5 – 7
x = 2.

### Question 3

#### Solution 3

As per the law of bracket of indices:

(am)n = am x n

On substituting values: a = 15, m = 3, n = n and (m x n) = 9

m x n = (m x n) => 3 x n = 9
=> n = 9/3
n = 3.

### Question 4

#### Solution 4

As per the law of negative power:

a-m = 1/am

On substituting values: a = 0.04, m = 2.5
=> (1/0.04)2.5
=> (100/4)2.5 (Removing decimals)
=> (25)2.5 => ((5)2)2.5
=> (5)5 (From the law of Bracket) 2 x 2.5 = 5.
=> 3125

2401 = (7)4
=> 73x –2 = 74
=> 3x – 2 = 4
=> 3x = 6
=> x = 2.

(1/64)-5/6
=> 645/6
=> (26)5/6
=> 25
=> 32

(256)-1/4
=> ( 1/256)1/4
=> (( 1/4)4)1/4
=> 1/4
=> 0.25

### Question 8

#### Solution 8

52 * ((5)4)0.25
=> 52 * ((5)4)1/4
=> 52 * 5
=> 53
=> 125.

(243/32)4/5
=> ((3/2)5)4/5
=> (3/2)4
=> 81 / 16

### Question 10

#### Solution 10

√((5/7)6x-4) = (7/5)2
=>(5/7)6x-4 = (7/5)4 (Squaring on both side.)
=> (5/7)6x-4 = (5/7)-4
=> 6x – 2 = -4
=> 6x = -2
=> x = – 1/3

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