Exponential Functions

Powers to Know

100

2²

What is 4?

200

4³

What is 64?

300

5⁴

What is 625?

400

10¹⁰

What is 10,000,000,000/10 billion?

500

2⁷

What is 128?

Evaluate (w/out cal)

100

64^-(3/4)

What is 1/4?

200

x^(3/4)=8

What is x=16?

300

x^(5/4)+36=4

What is x=no sol?

400

(x+5)^(2/3)=64

What is x=507?

500

3x^3/4=x^1/2

What is x=1/81?

Simplify

100

x⁴y³x²y⁸

What is x⁶y¹¹?

200

(5x²)³/100x⁵

What is 5x/4?

300

 (a¹¹/b¹¹)⁵(b⁹/a⁷)⁷

what is a⁶b⁸?

400

(35x³y²z) / (7xy⁴)

What is 5x²y^-2z or 5x²z/y²?

500

((6^p-4q)*(36^2p+p))/(6^5p-3q)

What is (6^p+3q+1)/p^4q

Rules

100

a^x+y 

What is a^x * a^y? 

200

a^m-n

What is a^m/aⁿ?

300

a⁰

What is 1?

400

(xy)^m

what is x^m*y^m?

500

a^-m

What is 1/a^m?

Evaluate

100

3^2x+1=81^x

What is x=1/2?

200

3^x+2=81^x-1

What is x=2?

300

2^3x+1=16^x-2

What is x=9?

400

5^x+1=125^2x

What is x=1/5?

500

10^2x-1=50

What is x≈1.349?