exam Maths Puzzle Numerical Ability

Show that the number(square root of 2 with exponent of square root of 2)with exponent of square root of 2 is a rational number even though it might look irrational. What familiar number does it equal?

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exam Other Question

Find the domain and range of the inverse of the given function.

f(x)=x^2-7; x>/= 0

I believe the answer is.. Domain and range are all real numbers? Am I correct? equation (1/5)-6=15625 in logarithm form
find the value of x log 2 32=x
express log (x+5) log as the logarithm of a single quanity