Simplify and express the result in power notation with positive exponent.

$(- 3)^{4} \times {(\frac{5}{3})}^{4}$ is $(m)^{4}$
$m = ?$

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Solution

We have
$(- 3)^{4} \times {(\frac{5}{3})}^{4}$
$= (- 1)^{4} \times (3)^{4} \times {(\frac{5}{3})}^{4}$
$= 3^{4} \times \frac{5^{4}}{3^{4}}$ [ $∵ (- 1)^{even number} = + 1, (\frac{a}{b})^{n} = \frac{a^{n}}{b^{n}}$ ]
$= (5)^{4}$
Thus, $m = 4$

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

$(- 3)^{4} \times {(\frac{5}{3})}^{4}$

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(iii) (iv)

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{(\frac{1}{2^{3}})}^{2}

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{(\frac{1}{2^{3}})}^{2}

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