ExponentsHUBBARD2016 | George's Blog

This is my assignment for exponents

Represent repeated multiplication with exponents.

This is the basics of exponents, an exponent is a number (base) multiplied by its own using a power (number of times multiplied)

Ex: $5^3 = 5x5x5$

2. Describe how powers represent repeated multiplication

Lets say $5^6$ , 5 would be the base and 6 would be the power, it would look like this; 5x5x5x5x5x5

3. demonstrate the difference between the exponent and the base by building models of a given power, such as $2^3$ and $3^2$

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 $3^2$

$2^3$ would be 2x2x2=8

$3^2$ would be 3×3=9

5. Evaluate powers with integral bases (excluding base 0) and whole number exponents.

Lets say $5^2 = 25$ or $1^{8327} = 1$ or $6^4= 1296$

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

$(-2^4)$ and $-2^4$ is the same thing, $-2\cdot-2\cdot-2\cdot-2= -16$

But when the base is in parentheses like $(-2)^4$ it would be $-1\cdot-2\cdot-2\cdot-2\cdot-2= 16$

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

$4^2\cdot4^3$ as you can see, we have the same base, we would not multiply the base and add the exponents together.

It would look like this $4^{2+3} = 4^5$

$4^3\div4^2$ as you can see, we have the same base, we would not divide the base and we would subtract the exponents.

It would look like this $4^{3-2} = 4^1$

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

$4^3\div2^3$ we can see here the base isn’t the same, that means we would divide the bases and keep the exponents.

It would look like this $(4\div2)^3 = 2^3 = 8$

9. Explain the law for power with an exponent of 0

Any positive base to the power of 0 would be 1

10. Use patterns to show that a power with an exponent of 0 is equal to 1

We can use the base of 5

$5^5=3125$ $5^4=625$ $5^3=125$ $5^2=25$ $5^1=5$ $5^0=1$

As you can see, each step down, the number divides by 5

11. Explain the law for powers with negative exponents

We divide the power by the base.

12. Use patterns to explain the negative exponent law

Lets say $5^{-1}$ this would be like $1\div5 = 0,2$

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

Yes, lets say $y^5\cdot y^3$ we would do $y^{5+3} = y^8$

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

Yes, lets say $5^7\cdot5^6 = 5^{7-6}$ , this would be wrong because it doesn’t correspond to the product rules, when you do multiply a power by the same base you add the exponents together and not subtract

15. Use the order of operations on expressions with powers

$(3^3)^4 = (3^3)\cdot(3^3)\cdot(3^3)\cdot(3^3)$

= $(3x3x3)\cdot(3x3x3)\cdot(3x3x3)\cdot(3x3x3)$

= $3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3\cdot3$

= $3^{12}=531441$

16. Determine the sum and difference of two powers

Sum

$5^2+6^2$ $25+36$ $= 61$

Difference:

$5^2-6^2$ $25-36$ $= -11$

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

$3\cdot9\cdot(\frac{4}{5}+5)$ $27\cdot(\frac{4}{5}+5)$ $27\cdot(5\frac{4}{5})$ $= 32\frac{4}{5}$

Here I did not use the BEDMAS rule correctly

18. Use powers to solve problems (measurement problems)

There is a rainfall in Congo, the millimeters of rain quintuples every hour and it started out with 5 millimeteres. How many millimeters of rain will there be in 1 hour? 2 hours? 5 hours?

1 hour: $5^1$ =5mm