Write in exponential form: - 2 7 - 3 × - 2 7 - 3 × - 2 7 - 3

To write the exponential form of - 2 7 - 3 × - 2 7 - 3 × - 2 7 - 3 . For a non-zero rational number a and for two integers m , n , we have a m × a n = a m + n . - 2 7 - 3 × - 2 7 - 3 × - 2 7 - 3 = - 2 7 - 3 + - 3 + 3 = - 2 7 - 9 Hence, the exponential form of - 2 7 - 3 × - 2 7 - 3 × - 2 7 - 3 = - 2 7 - 9

Express - 3 4 - 2 as a rational number.

To express - 3 4 - 2 as a rational number. Law of exponent: For a non-zero rational number a b and an integer m , we have a b - m = b a m . - 3 4 - 2 = 4 - 3 2 = - 4 3 × - 4 3 = 16 9 Therefore, - 3 4 - 2 = 16 9

Simplify 2 3 - 2 × - 7 8 0 .

To simplify 2 3 - 2 × - 7 8 0 . Laws of exponents: For a non-zero rational numer a b and an integer m , we have a b - m = b a m = b m a m a b 0 = 1 Now, 2 3 - 2 = 3 2 2 = 3 2 2 2 = 9 4 and - 7 8 0 = 1 So, 2 3 - 2 × - 7 8 0 = 9 4 × 1 = 9 4 Therefore, 2 3 - 2 × - 7 8 0 = 9 4

If a b = 2 3 - 3 × 5 6 0 , find the value of a b - 3 .

Given that a b = 2 3 - 3 × 5 6 0 , to find the value of a b - 3 . Laws of exponents: For a non-zero rational number x y and an integer m , we have x y - m = y x m x y 0 = 1 Now, 2 3 - 3 = 3 2 3 and 5 6 0 = 1 So, a b = 2 3 - 3 × 5 6 0 = 3 2 3 × 1 = 3 2 3 ⇒ a b - 3 = 3 2 3 - 3 = 3 2 - 9 = 2 3 9 Therefore, a b - 3 = 2 3 9

Find the value of x , if 5 6 7 × 5 6 - 9 = 5 6 2 x .

Given that 5 6 7 × 5 6 - 9 = 5 6 2 x , to find the value of x . Laws of exponents: For a non-zero rational number a and integers m , n , we have a m × a n = a m + n a m = a n ⇒ m = n Now, 5 6 7 × 5 6 - 9 = 5 6 7 + - 9 = 5 6 - 2 So, 5 6 - 2 = 5 6 2 x ⇒ - 2 = 2 x ⇒ x = - 1 Therefore, x = - 1

E M B I B E

ICSE NUMBERS WIZ>Chapter 2 - Exponents (Powers)>Mental Maths

S K Gupta and Anubhuti Gangal Solutions for Chapter: Exponents (Powers), Exercise 4: Mental Maths

Author:S K Gupta & Anubhuti Gangal

S K Gupta Mathematics Solutions for Exercise - S K Gupta and Anubhuti Gangal Solutions for Chapter: Exponents (Powers), Exercise 4: Mental Maths

Attempt the practice questions on Chapter 2: Exponents (Powers), Exercise 4: Mental Maths with hints and solutions to strengthen your understanding. ICSE NUMBERS WIZ solutions are prepared by Experienced Embibe Experts.