Express the following in power notation: - 27 64

- 27 64 = - 3 3 4 3 [ sin c e − 27 = ( − 3 ) 3 a n d 64 = 4 3 ] = - 3 4 3

Express the following in power notation: - 27 64

- 27 64 = - 3 3 4 3 [ sin c e − 27 = ( − 3 ) 3 a n d 64 = 4 3 ] = - 3 4 3

Express the following in power notation: - 32 243

To Express - 32 243 in power notation. ⇒ - 32 243 = - 2 × - 2 × - 2 × - 2 × - 2 3 × 3 × 3 × 3 × 3 Since, a m × a n = a m + n = - 2 1 + 1 + 1 + 1 + 1 3 1 + 1 + 1 + 1 + 1 = - 2 5 3 5 = - 2 3 5 Therefore, The power notation of - 32 243 is - 2 3 5

Express the following in power notation: - 1 128

To Express - 1 128 in power notation. ⇒ - 1 128 = - 1 2 × 2 × 2 × 2 × 2 × 2 × 2 We know that, a m × a n = a m + n = - 1 2 1 + 1 + 1 + 1 + 1 + 1 + 1 = - 1 2 7 Since, Odd power of negative number is always negative. = - 1 2 7 Therefore, The power notation of - 1 128 is - 1 2 7

Express the following as a rational number: 2 3 5

To Express 2 3 5 as a rational number We know that, a b m = a m b m ⇒ 2 3 5 = 2 5 3 5 ⇒ 2 5 3 5 = 2 × 2 × 2 × 2 × 2 3 × 3 × 3 × 3 × 3 = 32 243 Therefore, The rational form of 2 3 5 is 32 243 .

Express the following as a rational number: - 8 5 3

To Express - 8 5 3 as a rational number We know that, a b m = a m b m ⇒ - 8 5 3 = - 8 3 5 3 ⇒ - 8 3 5 3 = - 8 × - 8 × - 8 5 × 5 × 5 = - 512 125 Therefore, The rational form of - 8 5 3 is - 512 125 .

Express the following as a rational number: - 13 11 2

Given, - 13 11 2 We use exponential notation to write repeated multiplication, such as a × a × a × a = a 4 . And the same pattern would hold true for any non-zero number or variable. - 13 11 2 = - 13 2 11 2 = - 13 × - 13 11 × 11 = 169 121

Express the following as a rational number: 1 6 3

To Express 1 6 3 as a rational number We know that, a b m = a m b m ⇒ 1 6 3 = 1 3 6 3 ⇒ 1 3 6 3 = 1 × 1 × 1 6 × 6 × 6 = 1 216 Therefore, The rational form of 1 6 3 is = 1 216 .