Rational and Radical Exponents

Change to Exponent Form

100

Write the radical in exponential form.

sqrt(19)

19^(1/2)

200

Write the radical in exponential form.

root(4)(81)

 

81^(1/4)=3

300

Write the log in exponential form.

log 100 = 2

10^(2)=100

400

Write the log in exponential form and solve

log (2x - 4) = 2

100 = 2x - 4

x = 52

500

Write the log in expanded form

root(3)(2x^4)

1/3log2+ 4/3 logx

Simplify logs

100

log₃81

 

4

200

Evaluate

log_x8 = 3 

x = 2

300

Simplify

log₄8

3/2

400

Simplify: 3log 10

3

500

Write the rational expression in radical form.

10^(log81)

81

Simplify Exponents

100

Simplify.  

32^(1/5)

2

200

Simplify.  

(x^7)/(x^8)

1/x

300

Simplify.

64^(-2/3)

1/16

400

Simplify.

(1/2)^(-3)

8

500

Simplify.

(8/125)^-(2/3)

25/4

Solve

100

Solve.

2^(3x+1)=8

x = 2/3

200

Solve.

log(x-3)= 2

x = 103

300

Solve.

3^(x-10)= 1/9

x = 8

400

Solve.

log (x) + log(x) = log (5x+14)

Factor!
(x+2)(x-7) = 0
x = 7

500

Solve:

log 3 - log 8x = log 5

x = 3/40

Calculator

100

ln 5

1.609

200

log₂7

2.807

300

e⁴

54.598

400

Solve.

5^x-2 = 8

3.292

500

Solve.

2 * 6^(3x-4) + 7 = 21

1.695