Question 1

812.5 x 94.5 ÷ 34.8 = 9?

Accepted Answer

812.5 X 94.5 ÷ 34.8 = 9? ⇒ 812.5 x 94.5 ÷ 34.8 = 9? Apply the law of Fractional Exponents and Laws of Exponents (am)n = am x n ----------------1 (am) x (an) = am + n-------------2 am ÷ an = am ? n----------------3 and if pX = pY then X will be equal to Y. means X = Y;----------------4 Apply Law 1 ⇒ (92)2.5 x 94.5 ÷ 32 x 2.4 = 9? ⇒ 95 x 94.5 ÷ 92.4 = 9? Apply law 2 and 3, ⇒ 9(5 + 4.5 - 2.4) = 9? ⇒ 9? = 97.1 Apply the Law 4 ∴ ? = 7.1

Question 2

√5 + ∛x = 3, then the value of x is?

Accepted Answer

√5 + ∛x = 3 Apply the law of Algebra Law. Square both side of equation. (√5 + ∛x)2 = 32 ⇒ 5 + ∛x = 9 ⇒ ∛x = 9 - 5 ⇒ ∛x = 4 Now cube the both side of equation, ⇒ ( ∛x ) 3 = 43 ⇒ x = (4)3 ⇒ x = 64

Question 3

If ( 5 + 2√3 ) / ( 7 + 4√3 ) = a + b√3, then the value of a and b is?

Accepted Answer

Given equation is, ( 5 + 2√3 ) / (7 + 4√3 ) Now Multiply and divide by ( 7 - 4√3 ) in above given equation. By Rationalization, we will get, [ ( 5 + 2√3 ) / ( 7 + 4√3 ) ] x [ ( 7 - 4√3 ) / ( 7 - 4√3 ) ] [ ( 5 + 2√3 ) x ( 7 - 4√3 ) ] / [ ( 7 + 4√3 ) x ( 7 - 4√3 ) ] Apply the formula and multiplication rule of algebra, ( P + Q ) x (R - S ) = P x R - P x S + Q x R - Q x S .................(1) ( a + b ) x ( a - b) = a2 - b2.......................................................(2) = ( 5 x 7 - 5 x 4√3 + 7 x 2√3 - 2√3 x 4√3 )/ ( 72 - (4√3)2 ) = 35 - 20√3 + 14√3 - 8 x 3 / ( 49 - 16 x 3 ) = ( 35 - 24 - 6√3 )/(49 - 48 ) = 11 - 6√3 ∵ ( 5 + 2√3 ) /( 7 + 4√3 ) = a + b√3 ∴ a + b√3 = 11 - 6√3 on equating the above equation and we get, or a = 11 and b = - 6

Question 4

The expression [(√2)√2]√2 gives

Accepted Answer

Given expression = [(√2)√2]√2 = (√2)(2)√2/2 = (√2)(2)1/√2 = (2)1/2 x 21/√2 = 2(2/21/√2) = (2)(2)(1/√2 - 1) which denotes a real number but not a rational number .

Question 5

Simplify ( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 )

Accepted Answer

Given equation is, ( 6a-2bc-3/4ab-3c2 ) ÷ ( 5a-3 b2c-1/3ab-2c3 ) Apply the algebra law a ÷ b = a x 1/b = ( 6a-2bc-3/4ab-3c2 ) x ( 3ab-2c3/5a-3 b2c-1 ) = ( 6a-2 bc-3 x 3ab-2c3) / ( 4ab-3c2 x 5a-3b2c-1 ) Apply the law of Fractional Exponents and Laws of Exponents (am)(an) = am+n am÷an=am-n Or am/an=am-n = 18a-2 + 1 b1 - 2 c -3 + 3 / 20a1 - 3 b-3 + 2 c2 - 1 = 9a-1b-1c0/ 10a - 2 b-1c1 = ( 9/10 ) a-1 + 2b-1 + 1 c0 - 1 = ( 9/10 ) a1b0 c-1 = ( 9/10 ) ac-1 [∵ b0 = 1]

Question 6

The value of 273 × 34 ÷ 310 is equal to :

Accepted Answer

Question 7

The expression ( - 1 ) 132 is equivalent to : 5- 1 + 3- 1

Accepted Answer

Question 8

The value of ( - 1 ) -(2/3) 125

Accepted Answer

25

Question 9

The value of ( 8 ) - ( 2 - 2 ) is :

Accepted Answer

Question 10

If 102/5 × 108/5 = 10n, the value of n is :

Accepted Answer

∵ 102/5 × 108/5 = 10n ⇒ 102/5 + 8/5 = 10n ⇒ 1010/5 = 10n ⇒ 102 = 10n ⇒ n = 2 Hence, the value of n is 2.

Question 11

The positive exponential function of a -3 a -4 is : a-5

Accepted Answer

Question 12

The value of ( 2 3 ) 2/3 x ( 3 3 ) is : 3 2 2 2

Accepted Answer

62/3

Question 13

The value of 12x2y4z3 ÷ (2xy2 × 3yz2) will be :

Accepted Answer

Question 14

The value of x -2 y -4 ÷ y -2 is : x-3 . y-1 x-1

Accepted Answer

Question 15

if √4 × 43/2 ÷ 4-3 = 2x, the value of x will be :

Accepted Answer

Surds and Indices Questions