## Chapter 1 Number Systems Exercise 1.6

Question 1: Find:

i) 64^{1/2}

ii)32^{1/5}

iii) 125^{1/3}

Answer:

i)

= (8^{2})^{1/2}

by (a^{m})^{n} = a^{mn}

= 8^{2 × 1/2}

= 8

ii)

= (2^{5})^{1/5}

by (a^{m})^{n} = a^{mn}

= 2^{5 × 1/5}

= 2

iii)

= (5^{3})^{1/3}

by (a^{m})^{n} = a^{mn}

= 5^{3 × 1/3}

= 5

Question 2: Find:

i) 9^{3/2}

ii) 32^{2/5}

iii) 16^{3/4}

iv) 125^{-1/3}

Answer:

i)

= (3^{2})^{3/2}

by (a^{m})^{n} = a^{mn}

= 3^{2 ×} ^{3/2}

= 3^{3}

= 27

ii)

= (2^{5})^{2/5}

by (a^{m})^{n} = a^{mn}

= 2^{5 ×} ^{2/5}

= 2^{2}

= 4

iii)

= (2^{4})^{3/4}

by (a^{m})^{n} = a^{mn}

= 2^{4 × }^{3/4}

= 2^{3}

= 8

iv)

= (5^{3})^{-1/3}

by (a^{m})^{n} = a^{mn}

= 5^{3 × }^{-1/3}

= 5^{-1}

by a^{-n} = 1/a^{n}

= 1/5

Question 3: Simplify:

i) 2^{2/3} × 2^{1/5}

ii) (1/3^{3})^{7}

iii) 11^{1/2}/11^{1/4}

iv) 7^{1/2} × 8^{1/2}

Answer:

i) 2^{2/3} × 2^{1/5}

by a^{m} × a^{n} = a^{m + n}

= 2^{2/3 + 1/5} (2/3 + 1/5 = 10 + 3/15 = 13/15)

= 2^{13/15}

= ^{15}√2^{13}

ii) (1/3^{3})^{7}

by (a^{m})^{n} = a^{mn}

= (1/3^{3})^{7}= 1/3^{3 × }^{7}

= 1/3^{21}

by a^{-n} = 1/a^{n}

= 3^{-21}

iii) 11^{1/2}/11^{1/4}

By a^{m}/a^{n} = a^{m - n}

= 11(^{1/2 – 1/4})

= 11^{2/4 – 1/4}

= 11^{1/4}

= ^{4}√11

iv) 7^{1/2} × 8^{1/2}

by a^{m} × b^{m} = (ab)^{m}

= (7 × 8)^{1/2}

= 56^{1/2}

= √56

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