Question

Simplify: $\sqrt[3]{27 ^{\frac{3}{2}} }$ × $\sqrt{3}$

Answer 1

Answer:

9

Step-by-step explanation:

$given \\ \sqrt[3]{ {27}^{ \frac{3}{2} } } \times \sqrt{3} \\ using \: formula >> \sqrt[m]{a} = {a}^{ \frac{1}{m} } \\ = ( {27}^{ (\frac{3}{2} \times \frac{1}{3} )} ) \times {3}^{ \frac{1}{2} } \\ = {27}^{ \frac{1}{2} } \times {3}^{ \frac{1}{2} } \\ using > > 27 = 3 \times 3 \times 3 = {3}^{3} \\ = {(3)}^{ 3 \times \frac{1}{2}} \times {3}^{ \frac{1}{2} } \\ = {3}^{ \frac{3}{2} } \times {3}^{ \frac{1}{2} } \\ using \: formula > > {a}^{m}\times{a}^{n} = {a}^{(m + n)} \\ = {3}^{( \frac{3}{2} + \frac{1}{2} )} \\ = {3}^{( \frac{3 + 1}{2} )} \\ = {3}^{ (\frac{4}{2} )} \\ = {3}^{2} \\ = 9$

Answer 2

Answer:

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