Question

2√2√2√729 = p then the value of p^20/162+5/2​

Answer 1

Step-by-step explanation:

2√2√2√729 = p then the value of p^20/162+5/2

Answer 2

$\displaystyle \sf{ \frac{ {p}^{20} }{162} + \frac{5}{2} } = \bf 4$

Given :

$\displaystyle \sf{ \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } = p }$

To find :

The value of

$\displaystyle \sf{ \frac{ {p}^{20} }{162} + \frac{5}{2} }$

Solution :

Step 1 of 3 :

Write down the given equation

Here the given equation is

$\displaystyle \sf{ \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } = p }$

Step 2 of 3 :

Find the value of p

$\displaystyle \sf{ \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } = p }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{729} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{9 \times 9 \times 9} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ \sqrt[3]{ {9}^{3} } } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ 9 } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ \sqrt[2]{ {3}^{2} } } }$

$\displaystyle \sf{ \implies p = \sqrt[4]{ 3 } }$

$\displaystyle \sf{ \implies {p}^{4} = 3 }$

$\displaystyle \sf{ \implies p = {3}^{ \frac{1}{4} } }$

Step 3 of 3 :

Find the value of the expression

$\displaystyle \sf{ \frac{ {p}^{20} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{{ ({p}^{4} )}^{5} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{{ (3)}^{5} }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{81 \times 3 }{162} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{ 3 }{2} + \frac{5}{2} }$

$\displaystyle \sf{ = \frac{ 3 + 5 }{2} }$

$\displaystyle \sf{ = \frac{ 8 }{2} }$

$\displaystyle \sf{ = 4 }$

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