Fractional exponents

Richay

New member
Joined
Mar 31, 2006
Messages
43
These are pretty tough.

Here's three different ones

1.) 16^-1/2

2.) (-27)^-2/2

3.)
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How do i solve them. I have no clue.
 
16 ^ -1/2

would equal (1)/Sqrt 16 = 1/4

The denominator in your fraction exponent became your index of your radical, and since it was a negative exponent you must move it down to the denominator to make it positive.

Can you try the rest?
 
I understand how you did that one.

So, if i have to find the sqrt then of 27 it's 5.196......

Do i round it or am i doing this wrong?
 
Don't use decimals if you can get away with it.

\(\displaystyle \L\\\sqrt{27}=\sqrt{3}\sqrt{9}=3\sqrt{3}\)

See?.
 
Hello, Richay!

Exactly where is your difficulty?
    \displaystyle \;\;You don't understand negative exponents?
    \displaystyle \;\;You don't understand rational (fractional) exponents?
    \displaystyle \;\;You can't do any algebra at all??

You're getting answers with decimals.
If you're going to use your calculator, what's the problem?

1)  1612\displaystyle 1)\;16^{-\frac{1}{2}}
A negative exponent "moves" the expression.
    \displaystyle \;\;If it is in the numerator, it moves to the denominator.
    \displaystyle \;\;If it is in the denominator, it moves to the numerator.
And we drop the "minus".

So:   1612  =  11612\displaystyle \;16^{-\frac{1}{2}} \;= \;\frac{1}{16^{\frac{1}{2}}}

You're expected to know that a 12\displaystyle \frac{1}{2} power means "square root".

So we have:   116=14\displaystyle \;\frac{1}{\sqrt{16}}\:=\:\frac{1}{4}


2)  (27)22\displaystyle 2)\;\frac{(-27)^{-2}}{2}
We have: \(\displaystyle \L\;\frac{(-27)^{-2}}{2} \;= \;\frac{1}{2\,\cdot\,27^2}\;=\;\frac{1}{2\,\cdot\,729}\;=\;\frac{1}{1458}\)


This one gets "moved up":   18134  =  8134\displaystyle \;\frac{1}{81^{-\frac{3}{4}}} \;= \;81^{\frac{3}{4}}

You're expected to know that a 34\displaystyle \frac{3}{4} power means: 3rd power, 4th root.

So we have: \(\displaystyle \:\sqrt[4]{81^3}\:=\:\left(\sqrt[4]{81}\right)^3\:=\:(3)^3\:=\:27\)
 
galactus said:
Don't use decimals if you can get away with it.

\(\displaystyle \L\\\sqrt{27}=\sqrt{3}\sqrt{9}=3\sqrt{3}\)

See?.

Yes. That helps me understand square roots better.

soroban said:
Hello, Richay!

Exactly where is your difficulty?
    \displaystyle \;\;You don't understand negative exponents?
    \displaystyle \;\;You don't understand rational (fractional) exponents?

    \displaystyle \;\;You can't do any algebra at all??

You're getting answers with decimals.
If you're going to use your calculator, what's the problem?

1)  1612\displaystyle 1)\;16^{-\frac{1}{2}}
A negative exponent "moves" the expression.
    \displaystyle \;\;If it is in the numerator, it moves to the denominator.
    \displaystyle \;\;If it is in the denominator, it moves to the numerator.
And we drop the "minus".

So:   1612  =  11612\displaystyle \;16^{-\frac{1}{2}} \;= \;\frac{1}{16^{\frac{1}{2}}}

You're expected to know that a 12\displaystyle \frac{1}{2} power means "square root".

So we have:   116=14\displaystyle \;\frac{1}{\sqrt{16}}\:=\:\frac{1}{4}


[quote:3424z9uw]2)  (27)22\displaystyle 2)\;\frac{(-27)^{-2}}{2}
We have: \(\displaystyle \L\;\frac{(-27)^{-2}}{2} \;= \;\frac{1}{2\,\cdot\,27^2}\;=\;\frac{1}{2\,\cdot\,729}\;=\;\frac{1}{1458}\)


This one gets "moved up":   18134  =  8134\displaystyle \;\frac{1}{81^{-\frac{3}{4}}} \;= \;81^{\frac{3}{4}}

You're expected to know that a 34\displaystyle \frac{3}{4} power means: 3rd power, 4th root.

So we have: \(\displaystyle \:\sqrt[4]{81^3}\:=\:\left(\sqrt[4]{81}\right)^3\:=\:(3)^3\:=\:27\)[/quote:3424z9uw]

I see how you did those. The second one throw me off though.
If we change (-27)^-2/2 to: (-27)^-2/3 Then how would it be solved?
 
"If we change (-27)^-2/2 to: (-27)^-2/3 Then how would it be solved?"
Same way:
-27^(-2) / 3 = 1 / 3(-27^2) = 1 / 3(729) = 2187

What do you not understand? Remember: a^(-p) = 1 / a^p
 
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