Simplify 2 5 ÷ 2 3 , using laws of exponents.

Given, 2 5 ÷ 2 3 . We know that, a m a n = a m - n ⇒ 2 5 ÷ 2 3 = 2 5 - 3 = 2 2 Hence, 2 5 ÷ 2 3 = 2 2 .

Simplify 18 8 ÷ 18 4 , using laws of exponents.

Given, 18 8 ÷ 18 4 . On applying the law's of exponents, we get ⇒ 18 8 ÷ 18 4 ⇒ 18 8 - 4 . . . . . [ ∵ a m a n = a m - n ] ⇒ 18 4 Hence, 18 8 ÷ 18 4 = 18 4 .

Simplify 9 5 × 3 5 , using laws of exponents.

Given, 9 5 × 3 5 . On applying the law's of exponents, we get ⇒ 9 5 × 3 5 ⇒ ( 9 × 3 ) 5 . . . . [ ∵ a m × b m = ( a × b ) m ] ⇒ 27 5 Hence, 9 5 × 3 5 = 27 5 .

Simplify 3 y × 12 y , using laws of exponents.

Given, 3 y × 12 y . On applying the law's of exponents, we get ⇒ 3 y × 12 y ⇒ ( 3 × 12 ) y . . . . [ ∵ a m × b m = ( a × b ) m ] ⇒ 36 y Hence, 3 y × 12 y = 36 y .

Simplify 25 6 × 5 6 , using laws of exponents.

Given, 25 6 × 5 6 . On applying the law's of exponents, we get ⇒ 25 6 × 5 6 ⇒ ( 25 × 5 ) 6 . . . . [ ∵ a m × b m = ( a × b ) m ] ⇒ 125 6 Hence, 25 6 × 5 6 = 125 6 .

Express 4 5 × 4 2 × 4 4 in exponential form, with a single base.

Given, 4 5 × 4 2 × 4 4 . On applying the law's of exponents, we get ⇒ 4 5 × 4 2 × 4 4 = 4 5 + 2 + 4 . . . . . . [ ∵ a m × a n = a m + n ] = 4 11 Hence, 4 5 × 4 2 × 4 4 = 4 11 .

Express 3 2 × 3 3 7 in exponential form, with a single base.

Given, 3 2 × 3 3 7 . On applying the law's of exponents, we get ⇒ 3 2 × 3 3 7 = 3 2 + 3 7 . . . . [ a m × a n = a m + n ] = ( 3 5 ) 7 = 3 5 × 7 . . . . . . [ ∵ ( a m ) n = a m × n ] = 3 35 Hence, 3 2 × 3 3 7 = 3 35 .

Express 5 2 × 5 8 ÷ 5 5 in exponential form, with a single base.

Given, 5 2 × 5 8 ÷ 5 5 . On applying the law's of exponents, we get ⇒ 5 2 × 5 8 ÷ 5 5 = 5 2 + 8 ÷ 5 5 . . . . [ ∵ a m × a n = a m + n ] = 5 10 ÷ 5 5 = 5 10 - 5 . . . . . [ ∵ a m a n = a m - n ] = 5 5 Hence, 5 2 × 5 8 ÷ 5 5 = 5 5 .

E M B I B E

Mathematics Standard 7 Term Il>Chapter 3 - Algebra>Exercise 3.1

Exercise 3.1

Author:Tamil Nadu Board

Tamil Nadu Board Mathematics Solutions for Exercise 3.1

Simple step-by-step solutions to Exercise 3.1 questions of Algebra from Mathematics Standard 7 Term Il. Also get 3D topic explainers, cheat sheets, and unlimited doubts solving on EMBIBE.