Question 84

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

The exponential form for
$(- 2)^{4} \times {(\frac{5}{2})}^{4} i s (5^{4}) .$

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Solution

True:

Using law of exponents,
$a^{m} \div a^{n} = (a)^{m - n} a n d {(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}}$

$∴ (- 2)^{4} \times {(\frac{5}{2})}^{4} = (- 1)^{4} (2)^{4} \times \frac{(5)^{4}}{(2)^{4}} = (2)^{4 - 4} \times 5^{4} = 2^{0} \times 5^{4} = 5^{4}$

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