Question

Sir/ma'am
que. If 121 raised to the power 1by3 = cube root 121. This is a theorem. State the name of the theorem?

Answer 1

Law of exponents
There’s nothing mysterious! An exponent is simply shorthand for multiplying that number of identical factors. So 4³ is the same as (4)(4)(4), three identical factors of 4. And x³ is just three factors of x, (x)(x)(x).
One warning: Remember the order of operations. Exponents are the first operation (in the absence of grouping symbols like parentheses), so the exponent applies only to what it’s directly attached to. 3x³ is 3(x)(x)(x), not (3x)(3x)(3x). If we wanted (3x)(3x)(3x), we’d need to use grouping: (3x)³.
Negative Exponents

A negative exponent means to divide by that number of factors instead of multiplying. So 4−3 is the same as 1/(43), and x-3 = 1/x3.
As you know, you can’t divide by zero. So there’s a restriction that x−n = 1/xn only when x is not zero. When x = 0, x−n is undefined.
A little later, we’ll look at negative exponents in the bottom of a fraction.
Fractional Exponents

A fractional exponent—specifically, an exponent of the form 1/n—means to take the nth root instead of multiplying or dividing. For example, 4(1/3) is the 3rd root (cube root) of 4.