Question

Find the value of (3√√0.000064)^5


`Find \: the \: value \: of \: \bigg(\sqrt[3]{ √(0.000064) } { \bigg)}^(5) \\`
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Answer 1

0.00032

Explanation:

The value of interest is ...

(((64×10^-6)^(1/2))^(1/3))^5 = (2^6×10^-6)^(5/6) = 2^5×10^-5 = 0.00032

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The applicable rules of exponents are ...

`\sqrt[n]{x}=x^(1/n)\\\\(x^a)^b=x^(ab)\\\\(xy)^a=x^ay^a`

Answer 2

Explanation:

`\sf \: We \: have : \bigg( \sqrt[3]{ √(0.000064) } {\bigg) }^(5) \\`

`\sf = \bigg( \sqrt[3]{ \sqrt{ \frac{64}{ {10}^(6) } } } { \bigg)}^(5) \\`

`\sf = \bigg( \sqrt[3]{ \sqrt{ \bigg( \frac{8}{ {10}^(3) } } \bigg)^(3) } \bigg)^(5) \\`

`\sf = \bigg( \sqrt[3]{ \frac{8}{ {10}^(3) } } \bigg)^(5) \\`

`\sf = \bigg( \sqrt[3]{ \frac{ {2}^(3) }{ {10}^(3) } } \bigg)^(5) \\`

`\sf = \bigg( \sqrt[3]{ \bigg( (2)/(10) \bigg)^(3) } \bigg) ^(5) \\`

`\sf = \bigg( \bigg( (2)/(10) \bigg) ^{3 * (1)/(3) } \bigg) ^(5) \\`

`\sf = \bigg( \bigg( (2)/(10) \bigg) ^{ \cancel {\bf{3 }}* \frac{1}{ \cancel{ \bf3} }} \bigg) ^(5) \\`

`\sf = \bigg( (2)/(10) \bigg) ^(5 )`

`\sf = \frac{ {2}^(5) }{ {10}^(5) } \\`

`\sf = (2 * 2 * 2 * 2 * 2)/(10 * 10 * 10 * 10 * 10) \\`

`\sf = (32)/(100000) \\`

`\bf= {\boxed{0.00032}} \\`

Another method:

`\sf \: \bigg( \sqrt[3]{ √(0.000064) } {\bigg) }^(5) \\`

`\sf =[ \big{{(0.0000 64) ^{ (1)/(2) } \big}} ^{ (1)/(3) } { ] }^(5) \\`

`\sf = (0.000064) ^{ (1)/(2) * (1)/(3) + * 5} \\`

`\sf = (0.000064 {)}^{ (5)/(6) } \\`

`\sf = \bigg( (64)/(1000000) \bigg)^{ (5)/(6) } \\`

`\sf = \bigg( \frac{ {2}^(6) }{ {10}^(6) } \bigg) ^{ (5)/(6) } \\`

`\sf = [ \bigg( (2)/(10) \bigg) ^(6) ] ^{ (5)/(6) }\\`

`\sf = \bigg( (2)/(10) \bigg) ^{6 * (5)/(6) } \\`

`\sf = \bigg( (2)/(10) \bigg) ^{ \cancel{ \bf6 }* \frac{5}{ \cancel{ \bf6}} } \\`

`\sf = \bigg( (2)/(10) \bigg) ^(5) \\`

`\sf = \frac{ {2}^(5) }{ {10}^(5) } \\`

`\sf = (2 * 2 * 2 * 2 * 2)/(10 * 10 * 10 * 10 * 10) \\`

`\sf = (32)/(100000) \\`

`\sf = \boxed{ \sf0.00032}Ans. \\`

`\textsf{Please let me know if have any other questions.}\\`