Question

Simplify = (5^0+6^0+7^0+ 8^0 ) ^1/2​

Answer 1

Answer:

Solved in picture

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Answer 2

$\displaystyle \sf{ {( {5}^{0} + {6}^{0} + {7}^{0} + {8}^{0} )}^{ \frac{1}{2} } = 2 }$

Given :

$\displaystyle \sf{ {( {5}^{0} + {6}^{0} + {7}^{0} + {8}^{0} )}^{ \frac{1}{2} } }$

To find :

The value of the expression

Formula :

$\displaystyle \sf{1. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

‌$\displaystyle \sf{2. \: \: {a}^{0} = 1}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {( {5}^{0} + {6}^{0} + {7}^{0} + {8}^{0} )}^{ \frac{1}{2} } }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf{ {( {5}^{0} + {6}^{0} + {7}^{0} + {8}^{0} )}^{ \frac{1}{2} } }$

$\displaystyle \sf{ = {( 1 + 1 + 1 + 1)}^{ \frac{1}{2} } }$

$\displaystyle \sf{ = {( 4)}^{ \frac{1}{2} } }$

$\displaystyle \sf{ = {( {2}^{2} )}^{ \frac{1}{2} } }$

$\displaystyle \sf{ = {( 2 )}^{ 2 \times \frac{1}{2} } }$

$\displaystyle \sf{ = {( 2 )}^{ 1} }$

$\displaystyle \sf{ = 2 }$