Simplify and write the answer as a power of 10 . ( 200 ) 8 × ( 50 ) 8

Consider the given expression ( 200 ) 8 × ( 50 ) 8 = 2 × 10 2 8 × 5 × 10 8 = 2 8 × 10 2 8 × 5 8 × 10 8 ∵ a × b m = a m × b m = 2 8 × 10 16 × 5 8 × 10 8 = 2 × 5 8 × 10 16 + 8 ∵ a × b m = a m × b m , a m × a n = a m + n = 10 8 × 10 24 = 10 32 ∵ a m × a n = a m + n Hence, ( 200 ) 8 × ( 50 ) 8 = 10 32

Simplify and write the answer as a power of 10 . ( 200 ) 8 × ( 50 ) 8

Consider the given expression ( 200 ) 8 × ( 50 ) 8 = 2 × 10 2 8 × 5 × 10 8 = 2 8 × 10 2 8 × 5 8 × 10 8 ∵ a × b m = a m × b m = 2 8 × 10 16 × 5 8 × 10 8 = 2 × 5 8 × 10 16 + 8 ∵ a × b m = a m × b m , a m × a n = a m + n = 10 8 × 10 24 = 10 32 ∵ a m × a n = a m + n Hence, ( 200 ) 8 × ( 50 ) 8 = 10 32

Simplify using laws of exponents. x 5 × x 10 × x 3

Consider the given expression x 5 × x 10 × x 3 We know that for m , and n whole numbers and any non-zero number a , we have a m × a n = a m + n ∴ x 5 × x 10 × x 3 = x 5 + 10 + 3 Hence, x 5 × x 10 × x 3 = x 58

Simplify using laws of exponents. y 3 5 × y 2 2 ÷ y 18

Consider the given expression y 3 5 × y 2 2 ÷ y 18 We know that for m , and n whole numbers and any non-zero number a , we have a m n = a m n ∴ y 3 5 × y 2 2 ÷ y 18 = y 15 × y 4 ÷ y 18 = y 15 + 4 ÷ y 18 ∵ a m × a n = a m + n = y 19 ÷ y 18 = y ∵ a m ÷ a n = a m - n Hence, y 3 5 × y 2 2 ÷ y 18 = y

Simplify using laws of exponents. 5 4 7 15 9

Consider the given expression 5 4 7 15 9 We know that for m , and n whole numbers and any non-zero number a , we have a m n = a m n ∴ 5 4 7 15 9 = 5 28 5 × 3 9 = 5 28 5 9 × 3 9 ∵ a × b m = a m × b m = 5 28 - 9 3 9 ∵ a m ÷ a n = a m - n = 5 19 3 9 Hence, 5 4 7 15 9 = 5 19 3 9

Write the following number in the standard form. 8 . 758 × 10 5 × 10 2

Given number is 8 . 758 × 10 5 × 10 2 Since the standard form of a number is k × 10 n where k lies between 1 and 10 , and n is an integer. ∴ 8 . 758 × 10 5 × 10 2 = 8 . 758 × 10 5 + 2 ∵ a m × a n = a m + n Hence, 8 . 758 × 10 5 × 10 2 = 8 . 758 × 10 7

Write the following number in the standard form. 10 6 × 0 . 001001000

Given number is 10 6 × 0 . 001001000 Since the standard form of a number is k × 10 n where k lies between 1 and 10 , and n is an integer. So, shifting the decimal point by 3 digits to the right we have 10 6 × 0 . 001001000 = 1 . 001000 × 10 6 × 10 - 3 = 1 . 001000 × 10 6 + - 3 ∵ a m × a n = a m + n ∴ 10 6 × 0 . 001001000 = 1 . 001000 × 10 3