Question

List all the properties of exponents and powers.
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Answer 1

Answer:

Formulas and properties of exponents

1. a0 = 1 (a ≠ 0) - zero exponent property

2. a1 = a - any number raised by the exponent 1 is the number itself

3. an · am = an + m - product of powers property

4. (an)m = anm - power of a power property

5. anbn = (ab)n - power of a product property

Answer 2

Answer:

In earlier chapters we introduced powers.

x3=x⋅x⋅x

There are a couple of operations you can do on powers and we will introduce them now.

We can multiply powers with the same base

x4⋅x2=(x⋅x⋅x⋅x)⋅(x⋅x)=x6

This is an example of the product of powers property tells us that when you multiply powers with the same base you just have to add the exponents.

xa⋅xb=xa+b

We can raise a power to a power

(x2)4=(x⋅x)⋅(x⋅x)⋅(x⋅x)⋅(x⋅x)=x8

This is called the power of a power property and says that to find a power of a power you just have to multiply the exponents.

When you raise a product to a power you raise each factor with a power

(xy)2=(xy)⋅(xy)=(x⋅x)⋅(y⋅y)=x2y2

This is called the power of a product property

(xy)a=xaya

As well as we could multiply powers we can divide powers.

x4x2=x⋅x⋅⧸x⋅⧸x⧸x⋅⧸x=x2

This is an example of the quotient of powers property and tells us that when you divide powers with the same base you just have to subtract the exponents.

xaxb=xa−b,x≠0

When you raise a quotient to a power you raise both the numerator and the denominator to the power.

(xy)2=xy⋅xy=x⋅xy⋅y=x2y2

This is called the power of a quotient power

(xy)a=xaya,y≠0

When you raise a number to a zero power you'll always get 1.

1=xaxa=xa−a=x0

x0=1,x≠0

Negative exponents are the reciprocals of the positive exponents.

x−a=1xa,x≠0

xa=1x−a,x≠0

The same properties of exponents apply for both positive and negative exponents.

In earlier chapters we talked about the square root as well. The square root of a number x is the same as x raised to the 0.5th power

x−−√=x−−√2=x1

HOPE IT HELPS YOU