Question

find the value of. 10÷8 power-1÷3

Answer 1

Answers to Questions on Power Functions

Question: Evaluate 81/3 and 8-1/3

Answer: 2, 1/2

Question: Evaluate 82/3 and 8-2/3

Answer: 4, 1/4

Question: Evaluate 45/2, 274/3and 16-3/2

Answer: 32, 81, 1/64

Return to Exercises

Question: In the table below you can see the values of three different functions. Two are power functions: one has the form f(t) = at2, while the other has the form f(t) = bt3. The third is an exponential function of the form f(t) = kbt. Which is which and how can you tell?

tF1(t)tF2(t)tF3(t)1.02.502.22.04.81.24.321.02.642.25.811.46.862.03.172.46.911.610.243.03.802.68.111.814.584.04.562.89.412.020.05.05.473.010.8

Answer: 
F1(t) is the cubic function;

F2(t) is the exponential function;

F3(t) is the quadratic function.

Here are some observations which lead to these conclusions.

All power functions ktp with p  0 are zero for t = 0. Thus F2cannot be a power function.

Assuming that F1(t) = ktn with n = 2 or n = 3, we can evaluate F1(1) to obtain k. In this case, k = 2.5.

Since F1(t) = (2.5)tn with n = 2 or n = 3, we can figure out n by evaluating at t = 1.2.

(2.5)(1.2)2 = 3.6 and (2.5)(1.2)3= 4.32,

so n = 3.

Return to Exercises

Question: Solve 3 x2.2 = 6.

Answer: x = 21/(2.2). Since 2.2 = 22/10 = 11/5, this is the same as x = 25/11.

Question: 3 x2.2 = -6.

Answer: x = (-2)1/(2.2). Since 2.2 = 22/10 = 11/5, this is the same as x = (-2)5/11 which is a well-defined real number. On the other hand, your calculator or computer algebra package will probably treat the exponent 1/(2.2) as a REAL number and, not caring that this is a rational number with an odd denominator, will feel that (-2)1/(2.2) is a complex number which is NOT real. You be the judge!

Question: x -4 = 1.7

Answer: x = (1.7) -1/4.

Question: x -4 = -1.7

Answer: x -4 = 1/x4 which is never negative for real numbers x, so this equation has no solution in any interpretation.

Power FunctionsField Guide HUBCQ DirectoryCQ Resources