Radical, Exponential & Logarithmic Functions

Simplifying Radical & Exponential Expressions

100

(-2)^-5

-1/32

200

sqrt(25x²y⁸)

5xy⁴

300

(x⁷(2x)³)/x⁶

8x⁴

400

cuberoot(64x⁶y²¹)

4x²y⁷

500

sqrt(96)

4rad(6)

Simplifying Log Expressions

100

log_2(16)

4

200

log_9(1/81)

-2

300

e^ln(5)

5

400

log(cuberoot(100))

2/3

500

log_5(1/sqrt(125))

-3/2

Rationalizing Denominators

100

2/sqrt(3)

2sqrt(3)/3

200

5x/cuberoot(4)

5xcuberoot(2)/2

300

6x⁵y²/cuberoot(4x²y)

3x⁴ycuberoot(2xy²)

400

3/(6 - sqrt(5))

(18 + 3sqrt(5))/31

500

(4 + sqrt(3))/(8 + sqrt(3))

(29 + 4sqrt(3))/61

Domains of Radical & Log Functions

100

f(x) = sqrt(x + 5) + 2

[-5, oo)

200

f(x) = cuberoot(2x - 4)

(-oo, oo)

300

f(x) = 2log(5x)

(0, oo)

400

f(x) = log_3(5x + 6) + 2x⁴

(-6/5, oo)

500

f(x) = sqrt(x + 3) + ln(x - 7)

(7, oo)

Combining Radical Expressions

100

2xcuberoot(4) - 7xcuberoot(4)

-5xcuberoot(4)

200

5sqrt(27x) + 4sqrt(3x)

19sqrt(3x)

300

3xfourthroot(32x⁵) - fourthroot(2x⁹)

5x²fourthroot(2x)

400

6xcuberoot(9x²y³z⁷) * xcuberoot(6x⁵y⁶z)

18x⁴y³z²cuberoot(2x²z²)

500

5y2cuberoot(16x5y7) + 8xcuberoot(54x2y13)

34xy4cuberoot(2x2y)