Which one of the following options is equal to the expression
${(\frac{3}{4})}^{5} \div {(\frac{5}{3})}^{5} ?$

{(\frac{3}{4} \div \frac{5}{3})}^{5}

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{(\frac{4}{3} \div \frac{3}{5})}^{5}

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(\frac{3}{4} \div \frac{5}{3})

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{(\frac{3}{4} \div \frac{3}{5})}^{5}

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Solution

The correct option is A ${(\frac{3}{4} \div \frac{5}{3})}^{5}$
If $a$ and $b$ are non-zero integers and $m$ any integer, then we have
$(\frac{a}{b})^{m} = \frac{a^{m}}{b^{m}} .$
i.e., $a^{m} \div b^{m} = (a \div b)^{m}$
$∴ {(\frac{3}{4})}^{5} \div {(\frac{5}{3})}^{5} = {(\frac{3}{4} \div \frac{5}{3})}^{5}$

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Question 28

In the following question, out of the four options, only one is correct. Write the correct answer.

${(\frac{3}{4})}^{5} \div {(\frac{5}{3})}^{5}$ is equal to

(a) ${(\frac{3}{4} \div \frac{5}{3})}^{5}$

(b) ${(\frac{3}{4} \div \frac{5}{3})}^{1}$

(d) ${(\frac{3}{4} \div \frac{5}{3})}^{10}$

Question 28

In the following question, out of the four options, only one is correct. Write the correct answer.

${(\frac{3}{4})}^{5} \div {(\frac{5}{3})}^{5}$ is equal to

(a) ${(\frac{3}{4} \div \frac{5}{3})}^{5}$

(b) ${(\frac{3}{4} \div \frac{5}{3})}^{1}$

(d) ${(\frac{3}{4} \div \frac{5}{3})}^{10}$

Choose the appropriate one among the options with respect to the algebraic expression $35 x y + 45 x + 5 y^{2} + 25 x y z$ .

${(\frac{3}{4})}^{5} \div {(\frac{5}{3})}^{5}$ is equal to

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