Question

Let us simplify some more questions using the exponent rules.
(i)
$3 \frac{1}{3} \times 3 \frac{2}{3}$
(ii)
$(5 ^{3} ) \frac{1}{5}$
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Answer 1

Answer:

9

5^3/5

this is the answer may be but I am not sure

Answer 2

Step-by-step explanation:

Given that:

$(i)3 \frac{1}{3} \times 3 \frac{2}{3}$

$(ii)(5 ^{3} ) \frac{1}{5}$

To find: simplify using the exponent rules.

$(i) {3}^{ \frac{1}{3} } \times {3}^{ \frac{2}{3} } \\ \\Sol: \: \: \because {a}^{b} \times {a}^{c} = {(a)}^{b + c} \\ \\ {3}^{ \frac{1}{3} } \times {3}^{ \frac{2}{3} } = {3}^{( \frac{1}{3} + \frac{2}{3} )} \\ \\ = {3}^{ \frac{1 + 2}{3} } \\ \\ = {3}^{ \frac{3}{3} } \\ \\ = {3}^{1} \\ \\ {3}^{ \frac{1}{3} } \times {3}^{ \frac{2}{3} } = 3$

$(ii)(5 ^{3} ) \frac{1}{5} \\ \\ Sol:\: { ({5}^{3} )}^{ \frac{1}{5} } \\ \\ = {5}^{ \frac{3}{5} }$

*Note: some mistakes in latex coding in question,that was corrected before answering.

Hope it helps you.