1) represent repeated multiplication with exponents.

written in power form, the repeated multiplication form of this power is 6x6x6, exponents are easier to visualize when working out an equation.repeated multiplication can get out of hand so writing it as an exponent makes it easier.

2) describe how powers represent repeated multiplication.

the base is 4 and the exponents is 7( ) this shows that you multiply 4, seven times by itself. 4x4x4x4x4x4x4

3) demonstrate the differtence between the exponent and the base by building models of a given power, such as and

when there is a 3 as an exponents it means the object is 3 dimentional and whenn its squared the object is 2 dimentional.

 

 

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

the exponent represents how many times you are multipying the number by itself.
5) Evaluate powers with integral bases (excluding base 0) and whole number exponents

multiply the numerator by however many times the exponent says. then multiply the denominator by however many times the exponent says.

6) Explain the role of parentheses in powers by evaluating a given set of powers such as (-2)^4, (-2^4), and -2^4.

 

where the power is in relation to the parentheses will affect the sum. when the exponent is outside the parentheses you multiply the base by how many times the exponent is. when the exponent is inside the parentheses or there are no parentheses around a negative number that number will always be negative.

7) Explain the exponent laws for multiplying powers with the same base

the exponent law for multiplying powers with the same base is called the product law. the base stays the same but you add the exponents to get the new exponent for the single power.

8) explain the exponent laws for dividing powers with the same base.

this is called the quotient law. the base stays the same but you subtract the exponents to get the new exponent for the single power.

9) explain the exponent law for raising a product and quotient to an exponent.

the exponent law for raising a product and quotient to an exponent is called the power law. again the base stays the same then you multiply the exponents to get the new exponent for the new single power.

10) explain the law for powers with an exponent of zero.

the law for powers with an exponent of zero is called the zero exponent law. any number with the exponent of zero will always be one. this is because the exponent indicates  the amount of times a number is being multiplied by. when the exponent is zero it means you are not multiplying it by itself, so it is the base number that is equal to one.