Surds and Indices, General Mathematics

Question: If` (9^n xx 3^5 xx (27)^3)/(3 xx (81)^4) = 27`, then, n equals :
A
0

B
2

C
3

D
4

Note: `(9^n xx 3^5 xx (27)^3)/(3 xx (81)^4)` `= 27 => (3^2n xx 3^5 xx (3^3)^3)/(3 xx (3^4)^4` `= 3^3` `= (3^2n xx 3^5 xx 3^9)/(3^1 xx 3^16)` `= 3^3 or 3^(2n + 5 + 9)` `= 3^3 xx 3^1 xx 3^16 or 3^(2n + 14)` `= 3^20 `:. 2n + 14` `= 20 or 2n` `= 6 or n = 3`
1. Report
Question: If ` (9^n (3^2) (3^(-n/2))^ (- 2) - 27^n)/(3^3m (2^3))= 1/27,` then
A
m - n = 2

B
m - n = 1

C
m - n = -2

D
m - n = -1

Note: Not available
1. Report
Question: If `((9^n (3^2) (3^(-n/2))^(-2) - 27^n))/(3^3m (2^3)) = 1/27,` then
A
m - n = 2

B
m - n = 1

C
m - n = -2

D
m - n = -1

Note: Not available
1. Report
Question: If `(9^n (3^2) (3^(-n/2))^-2 - 27^n)/(3^3m (2^3)) = 1/27,` then
A
m - n = 2

B
m - n = 1

C
m - n = -2

D
m - n = -1

Note: Not available
1. Report
Question: If` (sqrt(3))^5 xx 9^2 = 3^a xx 3sqrt(3),` then a equals :
A
2

B
3

C
4

D
5

Note: `(sqrt(3))^5 xx 9^2` `= 3^a xx 3sqrt(3) => (31^(1∕2)^5 xx (3^2)^2` `= 3^a xx 3^1 xx 3^(1/2)` `:. 3^(5∕2) xx 3^4` `= 3^a xx 3^1 xx 3^(1∕2) or 3^(5/2 + 4)` `= 3^((a + 1 + 1/2))` `or 3^(13∕2)` `= 3^(a + 3/2). So, a + 3/2` `= 13/2 or a = (13/2 - 3/2)` `= 5 `
1. Report
Question: The simplified form of`( x^(7/2) . sqrt(y^3))/(x^(5/2) . sqrt(y))` is :
A
`x^2/y`

B
`x^3/y^2`

C
`x^6/y^3`

D
`xy`

Note: Not available
1. Report
Question: `(1/(1 + x^(n - m)) + 1/(1 + x^(m - n)))` is equal to :
A
0

B
1

C
`1/2`

D
`x^(m + n)`

Note: Given Exp.` = (1/(1 + x^n/x^m) + 1 + x^m/x^n)` `= (x^m)/((x^m + x^n)) + (x^n)/((x^m + x^n))` `= ((x^m + x^n)/(x^m + x^n))` `= 1`
1. Report
Question: If x, y, z are real numbers then the value of
A
xyz

B
`sqrt(xyz)`

C
`1/(xyz)`

D
1

Note: `sqrt(x^(-1 y) . sqrt(y^(-1) z . sqrt(z^(-1) x` `= sqrt(x/y) . sqrt(z/y) . sqrt(x/z)` `= sqrt(y)/sqrt(x) xx sqrt(z)/sqrt(y) xx sqrt(x)/sqrt(z)` `= 1`
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Question: `(x^b/x^c)^(b + c - a) .(x^c/x^a)^(c + a - b) .(x^a/x^b)^(a + b - c) = ?`
A
`x^abc`

B
x^(a + b + c)`

C
`x^(ab + bc + ca)`

D
1

Note: `= x^(b - c)(b + c - a) .x^(c - a)(c + a - b) . x^(a - b)(a + b - c)` `= x^((b^2 - c^2) + (c^2 - a^2) + (a^2 - b^2)) . x^(- a(b - c) - b(c - a) - c(a - b)` `= x^0 . x^0 = 1`
1. Report
Question: If pqr = 1 then,`(1/(1 + p + q^-1) + 1/(1 + q + r^ -1) + 1/(1 + r + p^-1)) = ?`
A
`0`

B
`1/pq`

C
`pq`

D
`1`

Note: Given Exp.`q/(q + pq + 1) + r/(r + qr + 1) + p/(p + pr 1)` `= q/(q + pq + 1) + 1/(1 + q + pq) + pq/(pq + 1 q) [:. r = 1/pq]` `= (q + 1 + pq)/(q + 1 + pq)` `= 1`
1. Report

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Question: If` (9^n xx 3^5 xx (27)^3)/(3 xx (81)^4) = 27`, then, n equals :

Question: If ` (9^n (3^2) (3^(-n/2))^ (- 2) - 27^n)/(3^3m (2^3))= 1/27,` then

Question: If `((9^n (3^2) (3^(-n/2))^(-2) - 27^n))/(3^3m (2^3)) = 1/27,` then

Question: If `(9^n (3^2) (3^(-n/2))^-2 - 27^n)/(3^3m (2^3)) = 1/27,` then

Question: If` (sqrt(3))^5 xx 9^2 = 3^a xx 3sqrt(3),` then a equals :

Question: The simplified form of`( x^(7/2) . sqrt(y^3))/(x^(5/2) . sqrt(y))` is :

Question: `(1/(1 + x^(n - m)) + 1/(1 + x^(m - n)))` is equal to :

Question: If x, y, z are real numbers then the value of

Question: `(x^b/x^c)^(b + c - a) .(x^c/x^a)^(c + a - b) .(x^a/x^b)^(a + b - c) = ?`

Question: If pqr = 1 then,`(1/(1 + p + q^-1) + 1/(1 + q + r^ -1) + 1/(1 + r + p^-1)) = ?`