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

A and B can build a wall in `6(2)/(3)` days. If A's one day work is `1(1)/(4)` of one day work of B, find in 4 how many days A and B alone can build the wall.

Write each of the following in the simplest form:
(a³)⁵ x a⁴

Write each of the following in the simplest form:
a² x a³ ÷ a⁴

Write each of the following in the simplest form:

`"a"^(1/3) ÷ "a"^(-2/3)`

Write each of the following in the simplest form:
a^-3 x a² x a⁰

Write the following in the simplest form:
(b^-2 - a^-2) ÷ (b^-1 - a^-1)

Simplify the following and express with positive index:
3p^-2q³ ÷ 2p³q^-2

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)`