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Power of a Power

i Evaluate: 8...

Question

Question 4(i)
Evaluate:

$\frac{8^{- 1} \times 5^{3}}{2^{- 4}}$

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Solution

$\frac{8^{- 1} \times 5^{3}}{2^{- 4}} = \frac{(2^{3})^{- 1} \times 5^{3}}{2^{- 4}} [∵ (a^{m})^{n} = a^{m \times n}] = \frac{2^{- 3} \times 5^{3}}{2^{- 4}} = 2^{- 3 - (- 4)} \times 5^{3} [∵ a^{m} \div a^{n} = a^{m - n}] = 2^{- 3 + 4} \times 5^{3} = 2 \times 125 = 250$

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Power of a Power

Standard VIII Mathematics

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