How do you solve 32 to the power of 2/5?

2 Answers
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

35
Nov 6, 2015

Answer:

Your final answer is 4.

Explanation:

#x = (32)^(2/5)# can be solved by using the exponent rule for fractional exponents: #x^(m/n) = root(n)(x^m)#. So, we can rewrite #(32)^(2/5)# as #root(5)(32^2)#

#32^2# evaluates to 1024, and #root(5)(1024)#, or the 5th root of 1024 (what times itself 5 times equals 1024) equals 4.

Was this helpful? Let the contributor know!
1500
Write your answer here...
Start with a one sentence answer
Then teach the underlying concepts
Don't copy without citing sources
preview
?

Answer

Write a one sentence answer...

Answer:

Explanation

Explain in detail...

Explanation:

I want someone to double check my answer

Describe your changes (optional) 200

15
Sep 16, 2017

Answer:

#4#
There is a choice of methods.. Work smarter, not harder!

Explanation:

One of the laws of indices deals with cases where there are powers and roots at the same time.

#x^(p/q) = rootq(x^p) = (rootq x)^p #

Note that the power can be inside or outside the root.

I prefer to find the root first, and then raise to the power because this keeps the numbers smaller. They can usually be calculated mentally rather than needing a calculator

#32^(2/5) = (color(red)root5(32))^2#

=#color(red)(2)^2color(white)(wwwwwwwwwwwww)(2*2*2*2*2=2^5=32)#

=#4#

Compare this with the other method of squaring first.

#root5(color(blue)(32^2)) = root5(color(blue)(1024))#

=#4#

While I know that #2^5 = 32 #, the square of #32# and the fifth root of #1024# are not facts that I would be able to recall from memory.

Was this helpful? Let the contributor know!
1500
Trending questions
Impact of this question
14788 views around the world
You can reuse this answer
Creative Commons License