SOLUTION: How do you multiply two eponential powers to the 4th root, sush as: 3 to the 4th root x 729 to the 4th root?

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Question 112648This question is from textbook Algebra 2 An Integrated Approach
: How do you multiply two eponential powers to the 4th root, sush as: 3 to the 4th root x 729 to the 4th root? This question is from textbook Algebra 2 An Integrated Approach

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Use the multiplication rule for radicals:
+sqrt%28a%29%2Asqrt%28b%29+=+sqrt%28ab%29+ provided a and b are not both negative numbers!

Likewise root%28n%2Ca%29%2Aroot%28n%2Cb%29+=+root%28n%2Cab%29+

In your specific case, root%284%2Ca%29%2Aroot%284%2Cb%29+=+root%284%2Cab%29+

Meanwhile, since you are doing a fourth root, be looking for perfect 4th powers that may be factors of these numbers. In particular, look for 2%5E4=16 and 3%5E4=+81. In this case, notice that 729 is divisible by 81, and can be written 729 = 81*9.

root%284%2C3%29%2Aroot%284%2C729%29+
+root%284%2C3%29%2Aroot%284%2C81%29%2Aroot%284%2C9%29+
root%284%2C3%29+%2A3%2A+root%284%2C9%29
3%2Aroot%284%2C3%29%2Aroot%284%2C9%29+
3%2Aroot%284%2C27%29+

For additional explanation on roots, please see my Lesson Plan in algebra.com. Or even better, go to my own website by clicking on my tutor name "rapaljer" anywhere in algebra.com. Click on my first link, which is "Basic or Intermediate Algebra: One Step at a Time", and look in Chapter 5 for Section 5.02 "Cube Roots and More". Also see my MATH IN LIVING COLOR PAGES. Look for Basic Algebra Chapter 5 or for more advanced problems see Intermediate Algebra Chapter 3. I think you will find this website helpful.

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