Question

How are exponents related to taking the root of a number? Use the inverse operation to evaluate perfect squares Express roots using fractions as exponents Approximate roots of non perfect squares

Answer 1

The root of a number asks of you, what number must be multiplied times itself to give you this number.
\[\sqrt{9}=3 because 3*3=9 or 3^{1+1}=3^2=9\]
\[\sqrt{x^6}=x^3 because x^3*x^3=x^6 or x^{3+3}\]
When you multiply, the exponents get added, since it's the same number, it's like multiplying the exponent times 2.
x^3*x^3=X^(3*2)
So to do the opposite operation (taking a square root), you have to divide by 2 or multiply times 1/2.
sqrt(x^6)=x^(6*1/2) or x^3
When you raise a number you multiply the exponents, so raising to 1/2 is like having the exponent multiply times 1/2
(x^6)^1/2=x^(6*1/2)=x^3

Answer 2

thank you