Question

n√a= ( )
(a)(a)n/2.
(b)(a)a
(c)(a)¹/n
(d)(a)√n​

Answer 1

Step-by-step explanation:

Basic rules for exponentiation

If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication

xn=x×x×⋯×xn times.

We can call this “x raised to the power of n,” “x to the power of n,” or simply “x to the n.” Here, x is the base and n is the exponent or the power.

From this definition, we can deduce some basic rules that exponentiation must follow as well as some hand special cases that follow from the rules. In the process, we'll define exponentials xa for exponents a that aren't positive integers.

The rules and special cases are summarized in the following table. Below, we give details for each one.

Rule or special case Formula Example

Product xaxb=xa+b 2223=25=32

Quotient xaxb=xa−b 2322=21=2

Power of power (xa)b=xab (23)2=26=64

Power of a product (xy)a=xaya 36=62=(2⋅3)2=22⋅32=4⋅9=36

Power of one x1=x 21=2

Power of zero x0=1 20=1

Power of negative one x−1=1x 2−1=12

Change sign of exponents x−a=1xa 2−3=123=18

Fractional exponents xm/n=xm−−−√n=(x√n)m 43/2=(4√)3=23=8