Surds and Indices, General Mathematics

Question: The value of `sqrt(8)^(1/3)` is:
A
`2`

B
`4`

C
`sqrt(2)`

D
`8`

Note: `(sqrt(8))^(1/3) ` `=(8^(1/2))^(1/3) ` `= 8^((1/2 xx 1/3)) ` `= 8^(1/6) ` `= 2^(3 xx 1/6) ` `= 2^(1/2) ` `= sqrt(2)`
1. Report
Question: The value of `5^(1/4) xx (125)^0.25` is
A
`sqrt(5)`

B
`5sqrt(5)`

C
5

D
25

Note: `5^1∕4 xx (125)^0.25` `= 5^0.25 xx (5^3)^0.25` `= 5^0.25 xx 5^(3 xx 0.25)` `= 5^0.25 xx 5^0.75` `= 5^(0.25 + 0.75)` `= 5^1` `= 5`.
1. Report
Question:
A

B

C

D

Note: Not available
1. Report
Question: The value of `5^1∕4 xx (125)^0.25` is ;
A
`sqrt(5)`

B
`5sqrt(5)`

C
`5`

D
`25`

Note: `5^1∕4 xx (125)^0.25` `= 5^0.25 xx (5^3)^0.25` `= 5^0.25 xx 5^(3 xx 0.25)` `= 5^0.25 xx 5^0.75` `= 5^(0.25 + 0.75)` `= 5^1` `= 5`.
1. Report
Question: The value of` (32/243)^(-4∕5)` is :
A
`4/9`

B
`9/4`

C
`16/8`

D
`81/16`

Note: `(32/243)^(-4∕5)` `= (243/32)^(4∕5)` `= (3^5/2^5)^(4∕5)` `= [(3/2)^5]^(4∕5)` `= (3/2)^(5 xx (4/5)` `= (3/2)^4` `= (3^5/2^5)^(4∕5)` `= [(3/2)^5]^(4∕5)` `= (3/2)^4` `= 3^4/2^4` `= 81/16`
1. Report
Question: `(1/216)^(-2∕3) ÷ (1/27)^(-4∕3)` = ?
A
`3/4`

B
`2/3`

C
`4/9`

D
`1/8`

Note: `(1/216)^(-2∕3) ÷ (1/27)^(-4∕3)` `= (216)^(2∕3) ÷ (27)^(4∕3)` `= (6^3)^(2∕3) ÷ (3^3)^(4∕3)` `= 6^(3 xx 2/3) ÷ 3^(3 xx 4/3)` `= 6^2 ÷ 3^4` `= 36/81` `= 4/9`
1. Report
Question: `(2^(n + 4) - 2.2n)/(2.2^(n + 3)) + 2^-3` is equal to :
A
`2^n + 1`

B
`- 2^(n + 1) + 1/8`

C
`(9)/(8) - 2^n`

D
`1`

Note: Given Exp.` = (2^n . 2^4 - 2. 2^n)/(2 . 2^n . 2^3) + 1/2^3` `= (2^n (2^4 - 2))/(2^n (2 . 2^3)) + 1/2^3` `= ((16 - 2)/16 + 1/8)` `= (7/8 + 1/8)` `= 1`
1. Report
Question: If `5sqrt(5) xx 5^3 -: 5^(-3∕2) = 5^(a + 2)` the of a is :
A
4

B
5

C
6

D
8

Note: `(5sqrt(5) xx 5^3)/(5^(-3∕2)` `= 5^(a + 2) <=> (5^(3∕2) xx 5^3)/(5^(-3∕2)` `= 5^(a + 2)` `:. 5(3/2 + 3 + 3/2)` `= 5^(a + 2) or 5^6` `= 5^(a + 2)` `:. a + 2 = 6 or a = 4`
1. Report
Question: If `sqrt(n^n) = 64` then the value of n is :
A
2

B
4

C
6

D
12

Note: `sqrt(2^n) = 64 <=> 2^(n∕2)` `= 64 = 2^6` `:. n/2 = 6 or n = 12.`
1. Report
Question: `((0.6)^0 - (0.1)^-1)/((3/2^3)^-1 . (3/2)^3 + (- 1/3)^-1)` is equal is :
A
`- 3/2`

B
`- 1/2`

C
`2/3`

D
`3/2`

Note: Given Exp. `= (1 - (1/10)^-1)/((2^3/3) . (3/3)^3 + (-3)^1` `= (1 - 10)/(2^3/3 . 3^3/2^3 - 3)` `= -9/(9 - 3)` `= -9/6` `= -3/2.`
1. Report

First Prev 1 2 3 Next Last

Question: The value of `sqrt(8)^(1/3)` is:

Question: The value of `5^(1/4) xx (125)^0.25` is

Question:

Question: The value of `5^1∕4 xx (125)^0.25` is ;

Question: The value of` (32/243)^(-4∕5)` is :

Question: `(1/216)^(-2∕3) ÷ (1/27)^(-4∕3)` = ?

Question: `(2^(n + 4) - 2.2n)/(2.2^(n + 3)) + 2^-3` is equal to :

Question: If `5sqrt(5) xx 5^3 -: 5^(-3∕2) = 5^(a + 2)` the of a is :

Question: If `sqrt(n^n) = 64` then the value of n is :

Question: `((0.6)^0 - (0.1)^-1)/((3/2^3)^-1 . (3/2)^3 + (- 1/3)^-1)` is equal is :