1.Represent repeated multiplication with exponents: 2^3=2*2*2

2.Describe how powers represent repeated multiplication: in 2^3, the 2 represent the number being multiplied by itself, the 3 represent the number of times that it is multiplied

3&4.Demonstrate the difference between 2^3 and 3^2: in the first one 2 is being multiplied by itself for 3 times, but for the second one the 3 is being multiplied by itself for 2 times. 2^3=2*2*2=8, but 3^2=3*3=9

5.2^2=2*2

2^3=2*2*2

2*4=2*2*2*2

2^5=2*2*2*2*2

6.(-2)^4=(-2)*(-2)*(-2)*(-2)=16

(-2^4)=-2^4=-(2*2*2*2)=-16

7.For multiplying and dividing powers with same base, you keep the base. For multiplication, you add the power, and for division, you subtract the power. Ex: 3^2*3^5=3^7 3^7/3^2=3^5

8.Raising product to a power:

when you take a power to a power, you multiply the exponents, (*x^*^{a})^^{b}= *x^*^{a}^{*}^{b}

when raising expression to a power, you raise numbers of variables inside the bracket to the exponent then multiply them seperately, Ex: (*2a)^*^{4} = (2*a*)(2*a*)(2*a*)(2*a*) = (2 *2*2 * 2)(*a * a * a * a*) = (2^^{4})(*a^*^{4}) = 16*a^*^{4}

Raising quotient (fraction) to a power:

when raising quotient to a power, the numerator and the demoninator is each raised to the power then divided, Ex: (3/4)^3=(3/4)*(3/4)*(3/4)=3^3/4^3=27/64

9.Powers with an exponent of zero is always 1

10.3^3=27

3^2=9 27/3=9

3^1=3 9/3=3

3^0=1 3/3=1

11.For a power with negative exponent, you turn the exponent to a positive and make the power divided by 1. Ex: 3^-2=1/3^2

12.3^3=27

3^2=9 27/3=9

3^1=3 9/3=3

3^0=1 3/3=1

3^-1=1/3^1=1/3

13.x^0=x^(a-a)=x^a*x^(-a)=x^a*(1/x^a)=x^a/x^a=1

14.(a*b)^x=ab^x WRONG!

(a*b)^x=a^x*b^x CORRECT

15.(-2)^2+4*(3-2)

=4+4*1

=8

16.Sum: (2^3)+(3^2)

=8+9=17

Difference: (3^2)-(2^3)

=9-8=1

17.5-2^3=3^3=27 WRONG!

5-2^3=5-8=-3 CORRECT

18.the cube box is 2 meters in side length, what is the volume?

2^3=8 the box is 8 meter cubed in volume

19.a bacteria doubles every hour how many bacteria after 5 hours?

1*2^5=32 32 bacteria after 5 hours

20.a^(-3)*(4+6)

=(1/a^3)*10

=10/a^3