Question

Simplify
$\sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7 \sqrt{7} } } } } = 7 ^{x}$
Find x step by step
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Answer 1

Step-by-step explanation:

There are 5 √s or roots. Each root represents a power of 1/2

and x½• x½= x

so,

7^(1/2+ 1/4+ 1/8 +1/16+ 1/32) =7^(31/32)=7^x.

=> x=31/32.

in plain text, it should be written as

= 7½•7¼•7⅛•7^(1/16)• 7^(1/32)

Each root has a multiplicity of 1/2

2 roots mean 1/2²=1/4

3 roots mean 1/2³=1/8.

Hope it helps.