Question 2(iv)
Simplify and express the result in power notation with positive exponent:

$(3^{- 7} \div 3^{- 10}) \times 3^{- 5}$

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Solution

$(3^{- 7} \div 3^{- 10}) \times 3^{- 5} = 3^{- 7 - (- 10)} \times 3^{- 5} [∵ a^{m} \div a^{n} = a^{m - n}] = 3^{- 7 \div 10} \times 3^{- 5} = 3^{3} \times 3^{- 5} = 3^{3 + (- 5)} [∵ a^{m} \times a^{n} = a^{m + n}] = 3^{- 2} = \frac{1}{3^{2}} [∵ a^{- m} = \frac{1}{a^{m}}]$

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Question 2(iv)
Simplify and express the result in power notation with positive exponent:

$(3^{- 7} \div 3^{- 10}) \times 3^{- 5}$

Question 2(v)
Simplify and express the result in power notation with positive exponent:

$2^{- 3} \times (- 7)^{- 3}$

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Question 2(v)
Simplify and express the result in power notation with positive exponent:

$2^{- 3} \times (- 7)^{- 3}$

(3^{- 7} \div 3^{- 10}) \times 3^{- 5}

\frac{1}{(3)^{m}}

m

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