Exponents and Radicals

Rules

100

x^a*x^b

x^{a + b}

200

x^a/x^b

x^{a - b}

300

(xy)^a  = __________

x^ay^a

400

(x/y)^a = _______________

x^a/y^a

500

x^-n = _________

1/(x^n)

Evaluating Exponents

100

(5x^2)^3/(100x^5

(5x)/4

200

(a¹¹/b¹¹)⁵ (b⁹/a⁷)⁷

a⁶b⁸

300

((10p^12n^7)/(5p^3n^5))^6

64p⁵⁴n¹²

400

n^200/n^198

n²

500

(8n^1776)/(23n^1773)

(8n^3)/23

Evaluating Exponents

100

58713^1/8

3.945

200

7x^-3 .  8x⁹

56x⁶

300

(4x³)² (-2x^-3y^-1)³

-128/(x^3y^3)

400

(490x¹⁷y²³)⁰

1

500

(1001x^-4y^-3)/(77x^6y^-7)

(13y^4)/x^10

Evaluating Radicals Mentally

100

root(6)(256) div root(4)(64)

2^frac1(6)

200

216^4/3

1296

300

36^3/2

216

400

64^x = 4

x = 1/3

500

root (3)root(4)root(5)(7)

root(60)(7) or 7^frac(1)(60)

Scientific Notation

100

Write 372,000 in scientific notation

3.72 x 10⁵

200

Write 4.68 x 10⁸ in standard form

468,000,000

300

Write 0.0005423 in scientific notation

5.423 x 10^-4

400

Write 24.7 billion in scientific notation

2.47 x 10¹⁰

500

Give me a thorough proof that anything to the 0 power is 1

2⁴ = 16            4³/4³ = 4⁰ or 1

4³ = 64

4² = 16

4¹ = 4

4⁰ = 1

4^-1 = 1/4