SOLUTION: How do you rewrite an expressions like 16^3/4? How do you simplifly 64^2/3, 25^5/2, and 81^7/4 by doing two steps ? how do you calculate the value of each of these expressions?

Question 233638: How do you rewrite an expressions like 16^3/4?
How do you simplifly 64^2/3, 25^5/2, and 81^7/4 by doing two steps ? how do you calculate the value of each of these expressions?
How do you solve each of the following equations for x: 2^1.4=2^x, 8^x=4, 3^5x=9^2

Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
For a fractional exponent, take the ROOT of the denominator, and RAISE to the power of the numerator.

Take the cube root of 64, and then square the result.

Take the square root of 25, and then raise the result to the 5th power.

Take the 4th root of 81, and then raise the result to the 7th power.

Since the base number is the same, the exponent must be the same, so 1.4 = x.

In the next two problems, you have to get the base numbers to be the same. In the first, express both sides as 2 raised to a power.

Therefore, 3x=2, so x=2/3

Likewise,

You finish it!

I have a complete explanation of exponential and logarithmic equations. Please visit my website by doing a "Bing" or "Google" search for my last name "Rapalje". Near the top of the search list, look for "Rapalje Homepage." Near the top of my Homepage, look for the link "Basic, Intermediate, and College Algebra". Choose "College Algebra". See Chapter 4, where you will find an entire chapter with my own non-traditional explanation, examples, exercises, and answers. This explanation is supported by my "MATH IN LIVING COLOR" pages, where the most difficult exercises are solved IN COLOR.

In addition, TWO videos of me explaining LOGARITHMS (from my own classes a few years ago!) are available FREE. To see the videos, from my Homepage look for the link "Rapalje Videos in Living Color", click on "College Algebra" and look for the topics on Logarithms.

Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus

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