Surds and Indices Questions Solved

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Surds and Indices Questions Solved

Below are the few Surds and Indices Questions Solved:

Question 1

(139)⁷ × (139)^x = (139)¹⁰. Find the Value of x?

Solution 1

As per the law of multiplication of indices:

a^m x aⁿ = a^m+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

(81)⁷ / (81)^x = (81)⁵. Find the Value of x?

Solution 2

As per the law of the division of indices:

a^m / aⁿ = a^m-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

(15³)ⁿ = 15⁹. Find Value of n?

Solution 3

As per the law of bracket of indices:

(a^m)ⁿ = a^{m 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

(0.04)^-2.5 = x. Find the Value of x?

Solution 4

As per the law of negative power:

a^-m = 1/a^m

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

Question 5

7^{3x –2} = 2401. Find value of x?

Solution 5

2401 = (7)⁴
=> 7^{3x –2} = 7⁴
=> 3x – 2 = 4
=> 3x = 6
=> x = 2.

Question 6

Simplify: (1/64)^-5/6 

Solution 6

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

Question 7

Simplify: (256)^-1/4

Solution 7

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

Question 8

5² * (625)^0.25 = x. Find the value of x?

Solution 8

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

Question 9

(32/243)^-4/5 = x. Find the value of x?

Solution 9

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

Question 10

√((5/7)^6x-4) = 49/25. Find value of x?

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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