Rational Exponents: write Y^10 under radical as exponential,

John Whitaker

Junior Member
Joined
May 9, 2006
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It's been a while, and I forgot how to express a radical.

Instruction: Write each radical as an exponential and symplify.
Problem displays Y^10 under a radical. Answer given is Y^5. What are the steps in determining this answer? (I usually do pretty well with these.)

Thank you
 
Re: Rational Exponents

Basic rule: \(\displaystyle \sqrt{a^2}=a\)

\(\displaystyle \sqrt{y^{10}}=\sqrt{y^5\cdot y^5}=\sqrt{(y^5)^2}=y^5\)

I will note that depending on your textbook's assumptions, it may give the basic rule as \(\displaystyle \sqrt{a^2}= | a |.\)
If this is the case, then your answer would be |y[sup:eek:qk29r1j]5[/sup:eek:qk29r1j]|.
 
Re: Rational Exponents

John Whitaker said:
Problem displays Y^10 under a radical.
John, next time show these like this: sqrt(Y^10)
 
Re: Rational Exponents

Thank you, Denis...

Another: My text, Lial, Hornsby, et al, assumes I know more than I do and takes leaps over steps I need. I get down to:

X^-8/3-4/3 Y^4-(-2/9)

and I don't understand how they get from there to:

X^-4 Y^38/9

I don't get the Y part.
 
Re: Rational Exponents

John Whitaker said:
Thank you, Denis...

Another: My text, Lial, Hornsby, et al, assumes I know more than I do and takes leaps over steps I need. I get down to:

X^-8/3-4/3 Y^4-(-2/9)

and I don't understand how they get from there to:

X^-4 Y^38/9

I don't get the Y part.

You should start a new thread (new topic) with new problem

\(\displaystyle 4 \, - \, (-\frac{2}{9}) \, = \, 4 \, + \, \frac{2}{9} \, = \, \frac{36}{9} \, + \, \frac{2}{9} \, = \, \frac{38}{9}\)
 
John Whitaker said:
... Lial, Hornsby, et al, assumes [sic] I know more than I do and takes [sic] leaps over steps I need ...


Hello John:

Making assumptions about what others assume is dangerous, but I'll go out on a limb and assume that Lial, Hornsby, et al, assume that you possess a functioning brain capable of independent thought and reasoning, and, furthermore, that you have both the time and motivation to do so.

Cheers,

~ Mark :)

"Spoon feeding, in the long run, teaches us nothing but the shape of the spoon." ~ E. M. Forster

 
Re: Rational Exponents

John Whitaker said:
X^-8/3-4/3 Y^4-(-2/9)
John, that MUST be shown this way: X^(-8/3 - 4/3) Y^(4 - (-2/9))

Why? Well, as example:
x^a/b means x^a divided by b
x^(a/b) means x^(a divided by b)

By the way, -8/3 - 4/3 = -1(8/3 + 4/3) = -1(12/3) = -1(4) = -4 ; ok?
The -1 is usually not SHOWN, BUT(like the Holy Ghost) is there!
 
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