Question

4. Find the value of 4 raised to 3−8 raised 2.

Answer 1

Step-by-step explanation:

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, 274/3 and 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?

t F1(t) t F2(t) t F3(t)

1.0 2.5 0 2.2 2.0 4.8

1.2 4.32 1.0 2.64 2.2 5.81

1.4 6.86 2.0 3.17 2.4 6.91

1.6 10.24 3.0 3.80 2.6 8.11

1.8 14.58 4.0 4.56 2.8 9.41

2.0 20.0 5.0 5.47 3.0 10.8

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 F2 cannot 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

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Answer 2

${4}^{3} - {8}^{2}$

$= 64 - 64$

$= 0$

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