# Everything I know about exponents

1) Represent repeated multiplication with exponents

4x4x4x4x4 = 1024 $4^5$ = 1024

2) Describe how powers represent repeated multiplication

The large number 4 is called the base, and the small number 5 is called the exponent. The exponent corresponds to the number of times the base is used as a factor.

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

$3^2$ Represents SA and $2^3$ Represents Volume

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

3 x 3= 9 $3^2$ = 9      2 x 2 x 2 = 8 $2^3$ = 8

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

5 x 5 x 5 x 5 = 625 $5^4$ = 625   4 x 4 x 4 x 4 x 4 = 1024  $4^5$ = 1024

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

$(-2)^4$ = -2 x -2 x -2 x -2 = 16   $(-2^4)$ = (-1 x 2 x 2 x 2 x 2) = -16    $-2^4$ = -1 x 2 x 2 x 2 x 2 = -16

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

$4^2$$4^6$$4^8$ = 65536 When multiplying keep the base and add the exponents.

$4^5$ ÷ $4^3$$4^2$ = 16 When dividing keep the base and subtract the exponents.

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

2 x $(6^3)^2$$2^2$$6^6$ = 4 x 46656 = 186624 When multiplying keep the base and multiply the exponents. If there is a coefficient add the exponent to the coefficient.

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

When a power is raised to a zero exponent, the answer is 1, except when the base is zero

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

$2^4$ = 16 $2^3$ = 8 $2^2$ = 4 $2^1$ = 2  $2^0$ = 1

11) Explain the law for powers with negative exponents.

You would have to flip the number with the negative exponent. $\frac {2^{-1}}{1}$ = $\frac {1}{2^1}$

12) Use patterns to explain the negative exponent law.

$\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$ $\frac{1}{32}$ If I was dividing by 2 I wanted to go lower I would do continue the pattern. So it would go 2,4,8,16,32 and so on.

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

$(-2)^3$ = -8| $x^6$

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

$4^3$ x $4^4$ = $4^7$ People might mistake the answer to this question as $4^{12}$

15) Use the order of operations on expressions with powers

8 x $3^5$ = 1944 First you would do the exponent. So then the question will become 8 x 243 = 1944

16) Determine the sum and difference of two powers.

$3^6 \times 3^5$$3^{11}$ = 177147| $3^6 \div 3^5$$3^1$ = 3

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

(10 + 50) x 5 = 260 The correct answer is 300 because you have to do the brackets before the multiplication 60 x 5 = 300

18) Use powers to solve problems (measurement problems)

Find the volume for a cube that is 2 cm in length, width and height. $2^3$ = 8 cm

19) Use powers to solve problems (growth problems)

Bacteria grows very rapidly. start with 1 bacteria and the bacteria multiplies 3 times every 1 hour. how much bacteria will there be in 10 hours? $3^{10}$ = 59049 There will be 59049 bacteria in 10 hours.

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

$a^{-2}$ x ${a}^{-5}$$\frac{1}{a^2} \times \frac{1}{a^5}$$\frac {1}{a^7}$

Core Competencies Self-Assessment math-25rmzxd