Exponents!

Real Numbers

100

What kind of number is pi?

Irrational

200

What is the first whole number?

Zero

300

Is 1.65656565..... a rational number?

Yes

400

Is -1.2 an integer?

Yes

500

Is the square-root of 256 rational or irrational?

Rational

Multiplying

100

3a⁴ x 4a³

12a⁷

200

(2y)(5y³)(-7y^-2)

-70y²

300

16c^-6 x  .5c^-2

8c^-8 = 8/c⁸

400

-4(rs)(-5r⁶s^-3)

20r⁷s^-2= 20r⁷/s²

500

12(x)(-.25x²y^-5)(4x^-3y⁷)

12x⁰y² = 12y²

Dividing

100

r⁷ / r⁴

r³

200

a²b⁵ / ab²

ab³

300

24x⁶y^-3z⁷ / 3x⁶y⁴z⁵

8z²/y⁷

400

r^-3s^-2t⁸ / r^-6s⁵t⁸

r³ / r⁷

500

(xyz³ / 5²x⁹y⁴z⁶)⁰

1

Powers

100

(x^1/2 )⁴

x²

200

(x^-2y^-4)^-2

x⁴y⁸

300

(x⁴y^-4)^-2

y⁸/x⁸

400

(r¹⁰s⁸)² + (r⁵s⁴)⁴

2r²⁰s¹⁶

500

((a^-1b⁵c^-2)^-2 / (a⁴b^-2c^-2)^-3)³

a⁴²/ b⁴⁸c⁶

Simplifying and Converting Rational Exponents

100

Convert from exponential form to radical form:

x^3/8

The eighth root of x³

200

Convert from radical form to exponential form:

The 4th root of x⁹

x^9/4

300

Simplify to both exponential and radical form:

(x^1/3 )(x^4/3)

x^5/3 = cubed root of x⁵

400

Simplify to both exponential and radical form:

(the 3rd root of r²) x (the fifth root of r⁸)

r^2/3 x r^8/5 = r^34/15 = the fifteenth root of r³⁴

500

Simplify to both exponential and radical form:

(the 4th root of r⁸)² / (the 3rd root of r)²

(r²)² / (r^1/3)² = r⁴ / r^2/3 = r^10/3 = the cubed root of r¹⁰