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Whole Numbers

Write each of...

Question

Write each of the following products in exponential form:

(i) a × a × a × a × ..... 15 times
(ii) 8 × b × b × b × a × a × a × a
(iii) 5 × a × a × a × b × b × c × c × c
(iv) 7 × a × a × a.... 8 times × b × b × b ×.... 5 times
(v) 4 × a × a ×..... 5 times × b × b ×....12 times × c × c.... 15 times

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Solution

$(i) a^{15} (i i) 8 b^{3} a^{4} = 8 a^{4} b^{3} (i i i) 5 a^{3} b^{2} c^{3} (i v) 7 a^{8} b^{5} (v) 4 a^{5} b^{12} c^{15}$

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\frac{a b^{2} c^{3} \times a^{4} b^{5} c^{- 6}}{a^{- 7} b^{- 8} c^{9} \times a^{10} b^{11} c^{- 12} \times a^{13} b^{- 14} c^{15}}

Q. Simplify the following:
a)

{(a^{8} \times a^{5})}^{0}

{(b^{2})}^{4} \times b^{0}

- \frac{a^{- 3} b^{10} c^{8} \times b c^{8}}{{(b^{- 10} \times c^{6})}^{4}}

{[\frac{- a^{- 5}}{- a^{10} b^{- 9} c^{- 7} \times (a^{- 15} \times c^{0})}]}^{2}

Q. Write in the exponential form:

a \times a \times a \times a \times b \times b \times c \times c

\frac{a^{- 7} \times b^{- 7} \times c^{5} \times d^{4}}{a^{3} \times b^{- 5} \times c^{- 3} \times d^{8}}

A = {1, 2, 3}, B = {4, 5, 6, 7, 8},

C = {4, 6, 8, 10, 12},

n [(A \times B) - (A \times C)] =

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