(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Find the value of k in each of the following:

`(root(3)(8))^((-1)/(2)` = 2^k 

Find the value of k in each of the following:

`root(4)root(3)(x^2)` = x^k 

Find the value of k in each of the following:

`(sqrt(9))^-7 xx (sqrt(3))^-5` = 3^k 

Find the value of k in each of the following:

`(1/3)^-4 ÷ 9^((-1)/(3)` = 3^k 

If a = `2^(1/3) - 2^((-1)/3)`, prove that 2a³ + 6a = 3

If x = `3^(2/3) + 3^(1/3)`, prove that x³ - 9x - 12 = 0

If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0

If a^x = b^y = c^z and b² = ac, prove that y = `(2xz)/(z + x)`

Show that : `(1)/(1 + "a"^("p"- "q")) + (1)/(1 + "a"^("q"- "p")`

Find the value of (8p)^p if 9^{p + 2} - 9^p = 240.

If a^x = b^y = c^z and abc = 1, show that

`(1)/x + (1)/y + (1)/z` = 0.

If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)³ = 27xyz

If 2250 = 2^a. 3^b. 5^c, find a, b and c. Hence, calculate the value of 3^a x 2^-b x 5^-c.

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.

Find the value of 'a' and 'b' if:

9^2a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`

Find the value of 'a' and 'b' if:

`(sqrt243)^"a" ÷ 3^("b" + 1)` = 1 and `27^"b" - 81^(4 -"a"/2)` = 0

Prove the following:

`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1

Prove the following:

`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1

Prove the following:

`("a"^"m"/"a"^"n")^("m"+"n"+1) ·("a"^"n"/"a"^1)^("n" + 1-"m").("a"^1/"a"^"m")^(1+"m"-"n")`