Question 73

In the following question, state whether the given statements are true (T) or false (F).

${(\frac{2}{3})}^{- 2} \times {(\frac{2}{3})}^{- 5} = {(\frac{2}{3})}^{10}$

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Solution

False:

$L H S = {(\frac{2}{3})}^{- 2} \times {(\frac{2}{3})}^{- 5}$

Using law of exponents,
$a^{m} \times a^{n} = (a)^{m + n}$

$∴ {(\frac{2}{3})}^{- 2} \times {(\frac{2}{3})}^{- 5} = {(\frac{2}{3})}^{- 2 - 5} = {(\frac{2}{3})}^{- 7}$

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