Form the number from its expanded form given below: 9 × 10 4 + 5 × 10 3 + 6 × 10 2 + 7 × 10

We have to write the given expanded form in short form 9 × 10 4 + 5 × 10 3 + 6 × 10 2 + 7 × 10 . For this we need to convert the exponents in normal number form. ⇒ 9 × 10 4 + 5 × 10 3 + 6 × 10 2 + 7 × 10 = 9 × 10000 + 5 × 1000 + 6 × 100 + 7 × 10 Multiply the numbers to get the digits of different place values. ⇒ 90000 + 5000 + 600 + 70 Add the numbers to get the required short form of the given expanded form. ⇒ 90000 + 5000 + 600 + 70 = 95670 Hence, the number is 95670 .

Simplify and express it in power form: 2 3 × 3 5 × 16 3 × 32

We have to find the value of 2 3 × 3 5 × 16 3 × 32 . We can write 16 and 32 as power of 2 . ⇒ 2 3 × 3 5 × 16 3 × 32 = 2 3 × 3 5 × 2 4 3 × 2 5 If a is a non-zero integer and m and n are also integers, then a m × a n = a m + n . ⇒ 2 3 × 3 5 × 2 4 3 × 2 5 = 2 3 + 4 × 3 5 3 × 2 5 = 2 7 × 3 5 3 × 2 5 If a is a non-zero integer and m and n are also integers, then a m ÷ a n = a m a n = a m - n . ⇒ 2 7 × 3 5 3 × 2 5 = 2 7 - 5 × 3 5 - 1 = 2 2 × 3 4 = 2 2 × 9 2 If a and b are two integers and m is also an integer then a × b m = a m × b m . ⇒ 2 2 × 9 2 = 2 × 9 2 = 18 2 Hence, the required answer is 18 2 .

Simplify and express it in power form: 6 2 3 × 6 4 ÷ 6 7

We have to find the value of 6 2 3 × 6 4 ÷ 6 7 . If a is a non-zero integer and m and n are also integers, then a m n = a m × n . ⇒ 6 2 3 × 6 4 ÷ 6 7 = 6 2 × 3 × 6 4 ÷ 6 7 = 6 6 × 6 4 ÷ 6 7 If a is a non-zero integer and m and n are also integers, then a m × a n = a m + n . ⇒ 6 6 × 6 4 ÷ 6 7 = 6 6 + 4 ÷ 6 7 = 6 10 ÷ 6 7 If a is a non-zero integer and m and n are also integers, then a m ÷ a n = a m a n = a m - n . ⇒ 6 10 ÷ 6 7 = 6 10 - 7 = 6 3 Hence, the required answer is 6 3 .

Simplify and express it in power form: 4 5 × a 8 b 3 4 5 × a 5 b 2 b ≠ 0

We have to find the value of 4 5 × a 8 b 3 4 5 × a 5 b 2 . If x is a non-zero integer and m and n are also integers, then x m ÷ x n = x m x n = x m - n . ⇒ 4 5 × a 8 b 3 4 5 × a 5 b 2 = 4 5 - 5 × a 8 - 5 × b 3 - 2 = 4 0 × a 3 × b 1 If x is a non-zero integer then x 0 = 1 . ⇒ 4 0 × a 3 × b 1 = 1 × a 3 × b = a 3 b

Simplify and express it in power form: 2 8 × x 7 4 3 × x 3 x ≠ 0

We have to find the value of 2 8 × x 7 4 3 × x 3 . We can write 4 as 2 2 . ⇒ 2 8 × x 7 4 3 × x 3 = 2 8 × x 7 2 2 3 × x 3 If a is a non-zero integer and m and n are also integers, then a m n = a m × n . ⇒ 2 8 × x 7 2 2 3 × x 3 = 2 8 × x 7 2 6 × x 3 If a is a non-zero integer and m and n are also integers, then a m ÷ a n = a m a n = a m - n . ⇒ 2 8 × x 7 2 6 × x 3 = 2 8 - 6 × x 7 - 3 = 2 2 × x 4 If a and b are two integers and m is also an integer then a × b m = a m × b m . ⇒ 2 2 × x 4 = 2 2 × x 2 2 = 2 x 2 2 Hence, the required answer is 2 x 2 2 .

E M B I B E

GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 7>Chapter 5 - Concept of Index>Let's Work out

West Bengal Board Solutions for Chapter: Concept of Index, Exercise 18: Let's Work out

Author:West Bengal Board

West Bengal Board Mathematics Solutions for Exercise - West Bengal Board Solutions for Chapter: Concept of Index, Exercise 18: Let's Work out

Attempt the practice questions on Chapter 5: Concept of Index, Exercise 18: Let's Work out with hints and solutions to strengthen your understanding. GANITPRABHA (MATHEMATICS TEXT BOOK) CLASS 7 solutions are prepared by Experienced Embibe Experts.