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

Simplify the following and express with positive index:

`[("p"^-3)^(2/3)]^(1/2)`

Simplify the following:

`(27 xx^9)^(2/3)`

Simplify the following:

`(8 xx^6y^3)^(2/3)`

Simplify the following:

`((64"a"^12)/(27"b"^6))^(-2/3)`

Simplify the following:

`((36"m"^-4)/(49"n"^-2))^(-3/2)`

Simplify the following:

`("a"^(1/3) + "a"^(-1/3))("a"^(2/3) - 1 + "a"^(-2/3))`

Simplify the following:

`root(3)(x^4y^2) ÷ root(6)(x^5y^-5)`

Simplify the following:

`{("a"^"m")^("m" - 1/"m")}^(1/("m" + 1)`

Simplify the following:
`x^("m" + 2"n"). x^(3"m" - 8"n") ÷ x^(5"m" - 60)`

Simplify the following:

`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`

Simplify the following:

`(27/343)^(2/3) ÷ (1)/(625/1296)^(1/4) xx (536)/root(3)(27)`

Simplify the following:

`(5^x xx 7 - 5^x)/(5^(x + 2) - 5^(x + 1)`

Simplify the following:

`(3^(x + 1) + 3^x)/(3^(x + 3) - 3^(x + 1)`

Simplify the following:

`(2^"m" xx 3 - 2^"m")/(2^("m" + 4) - 2^("m" + 1)`

Simplify the following:

`(5^("n" + 2) - 6.5^("n" + 1))/(13.5^"n" - 2.5^("n" + 1)`

Express the following in the exponential form:
log₂ 128 = 7

Express the following in the exponential form:
log₃ 81 = 4

Express the following in the exponential form:
log₁₀ 0.001 = -3

Express the following in the exponential form:

`"log"_2 (1)/(32)` = -5

Express the following in the exponential form:
log_b a = c