# Every thing I know about exponent

1.      Represent repeated multiplication with exponent

For example: x*x*x*x=x^4

2.      Describe how powers represent repeated multiplication

For example: y^4=y*y*y*y

3.      Demonstrate difference between the exponent and the base by building model of a given power as 2^3 and 3^2

The power of 3^2 is 9 and the power of 2^3 is 8.From this, 3^2 isn’t same to 2^3

3^2 is 3*3

2^3 is 2*2*2

4.      Demonstrate difference between two given powers in witch the exponent and the base are interchanged by using repeated multiplication, such as 2^3 and 3^2

The cube of 2 means 2*2*2, and the square of 3 means 3*3.

So cube means multiply for two times and square means multiply one time.

5.      Evaluate power with integral based whole number exponent(excluding 0)

For example: a^m*a^n=a^(m+n)

a^w/a^y=a^(w-y)

(a^m)^n=a^mn

(ab)^m=a^m*b^m

(a/b)^n=a^n/b^n

6.      Explain the role of parentheses in powers by evaluating a given set of powers such as ab^2 and (ab)^2

(ab)^2=a^2*b^2 From this they aren’t same

7.      Explain the exponent laws for multiplying and dividing powers with the same base.

a^m*a^n=a^(m+n)

a^w/a^y=a^(w-y)

8.      Explain the exponent laws for raising a product and quotient to an exponent.

(ab)^m=a^m*b^m

(a/b)^n=a^n/b^n

9.      Explain the law for powers with an exponent of zero.

All the number with the exponent of zero are one (excluding zero)

10.  Use patterns to show that a power with an exponent of zero is equal to one.

All the number with the exponent of one are the number

11.  Explain the law for powers with negative exponent law.

When exponent is odd and the base is negative, the power must negative.

Otherwise, when exponent is even and the base is negative, the power must positive.

12.  Use patterns to explain the negative exponent law.

When exponent is negative result will be one over the base to power

13.  I can apply the exponent laws to powers with both integer and variable bases

Improve this, I’ll give two examples

E.g.1: (-7)^3 -7^3

(-7)^3=343

-7^3=-343

E.g.2: a^3/a^3=1

All the number with the exponent of zero are one

a^3/a^3=a^0=1

14.  I can identify the error in a simplification of an expression involving powers.

Using the exponent multiplying into the bracket

E.g. (3^4)^4 3^8

15.  Use the order of operations on expressions with powers.

Bracket has more priority than power

(2+3)^3=5^32+3^3

16.  Determine the sum and difference of two powers.

5^7+5^35^10

5^7-5^35^4

17.  Identify the error in applying the order of operations in an incorrect solution.

2/3(3-5)^2

=4/2(-2)^2

=2/(-2)^2

=(-1)^2

=1

18.  Use powers to solve problems (measurement problems)

A cube with side length of 10cm , what’s its volume?

Volume = side*side*side = side^3 = 10cm^3

Volume = 1000cm^3 19.  Use powers to solve problems (growth problems) A: 100*3^1=300   B: 100*3^2=900   C: 100*3^12=53144100     D: 100*3^n=3^n*100

20.  Applying the order of operations on expressions with powers involving negative exponents and variable bases.

(-9a^3*7a^8)^3-b^9/c^11=-63a^11-b^9/c^1113.