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Exponents

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Exponents

Gabriel Lucas - Math 70.08

Question

Guess

Answer

Important rules in blue

Answers in Red

(I may collect this)

Gabriel Lucas - Math 70.08

1. Rewrite using just the number 7

4·7

Gabriel Lucas - Math 70.08

A:7 + 7 + 7 + 7

Which one?

B:7 · 7 · 7 · 7

Gabriel Lucas - Math 70.08

A:7 + 7 + 7 + 7

Answer: A

because 4 · 7 = 4 sevens = 28

B:7 · 7 · 7 · 7

Gabriel Lucas - Math 70.08

2. Rewrite using just the letter d

3d

Gabriel Lucas - Math 70.08

A:d + d + d

Which one?

B:d · d · d

Gabriel Lucas - Math 70.08

A:d + d + d

Answer: A

because 3d = 3 d’s = d + d + d

B:d · d · d

Gabriel Lucas - Math 70.08

Rule 1

a(x) =

x + x + … + x + x

?

Gabriel Lucas - Math 70.08

Rule 1

a(x) =

x + x + … + x + x

a

Gabriel Lucas - Math 70.08

3. Rewrite using just the number 3

34

Gabriel Lucas - Math 70.08

A:3 + 3 + 3 + 3

Which one?

B:3 · 3 · 3 · 3

Gabriel Lucas - Math 70.08

A:3 + 3 + 3 + 3

Answer: B

because 34 = Multiply 3 times itself 4 times

B:3 · 3 · 3 · 3

Gabriel Lucas - Math 70.08

4. Rewrite using just the letter y

y5

Gabriel Lucas - Math 70.08

A:y + y + y + y + y

Which one?

B:y · y · y · y · y

Gabriel Lucas - Math 70.08

A:y + y + y + y + y

Answer: B

because y5 = Multiply y times itself 5 times

B:y · y · y · y · y

Gabriel Lucas - Math 70.08

Rule 2

xb =

x · x · … · x · x

?

Gabriel Lucas - Math 70.08

Rule 2

xb =

x · x · … · x · x

b

Gabriel Lucas - Math 70.08

5. Rewrite w/out the fraction

Gabriel Lucas - Math 70.08

Rule 3

Left hand side gets the 2

y2 = x5

Right hand side gets the 5

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

6. Rewrite w/out the fraction

Gabriel Lucas - Math 70.08

y7 = x3

Gabriel Lucas - Math 70.08

7. Rewrite w/out the fraction

Gabriel Lucas - Math 70.08

y2 = 811= __

Gabriel Lucas - Math 70.08

y2 = 811= __

Gabriel Lucas - Math 70.08

y2 = 811 = 81

Gabriel Lucas - Math 70.08

8. Solve for y

y2 = 81

y = __

Gabriel Lucas - Math 70.08

y2 = 81

y = 9 or -9

Gabriel Lucas - Math 70.08

9. If you saw...

…you could write

y = 81

(what’s missing?)

Gabriel Lucas - Math 70.08

If you saw...

…you could write

Gabriel Lucas - Math 70.08

Rule 4a

means

Gabriel Lucas - Math 70.08

10. Rewrite w/out the fraction

Gabriel Lucas - Math 70.08

y2 = 43

Gabriel Lucas - Math 70.08

y2 = 43

Solve for y

y = ___

Gabriel Lucas - Math 70.08

y2 = 43

Gabriel Lucas - Math 70.08

11. If you saw...

…you could write

y = ____

Gabriel Lucas - Math 70.08

If you saw...

…you could write

Gabriel Lucas - Math 70.08

Rule 4b

means

Gabriel Lucas - Math 70.08

y2 = x

yy = x

Gabriel Lucas - Math 70.08

y2 = x

y3 = x

yy = x

yyy = x

Gabriel Lucas - Math 70.08

y2 = x

y3 = x

yy = x

yyy = x

Gabriel Lucas - Math 70.08

ym = x

y2 = x

y3 = x

yy = x

yyy = x

y·…·y = x

Gabriel Lucas - Math 70.08

ym = x

y2 = x

y3 = x

yy = x

yyy = x

y·…·y = x

Gabriel Lucas - Math 70.08

Gabriel Lucas - Math 70.08

Rule 5

means

Gabriel Lucas - Math 70.08

Rule 6

ym ·yn = ym + n

(xy)m = xm · ym

xm ·ym = (xy)m

= ym - n

y0 = 1

(ym)n = ym · n

y1 = y

Gabriel Lucas - Math 70.08