Question

I need help with two questions involving exponential functions. the first one is about simplifying this expression; sqrt of 8 over sqrt of 8 to the 5'th power. The second expression is asked to be evaluated, and looks like this; sqrt of 5 times the sqrt of 5 to the third power over the sqrt of 5 to the fifth power, to the third power. They are both REALLY difficult for me.
Edit: here is a REAL representation of the equations;
#1:https://la.brainhoney.com/Resource/19773651,544,0,0/Assets/61083_51e84c3e/04_11_03.gif
#2:https://la.brainhoney.com/Resource/19773651,544,0,0/Assets/61083_51e84c3e/04_11_06.gif

Answer 1

\[\Huge {a^n \over a^m}=a^{n-m}\]

Answer 2

No. These are not exponential functions. In exponential functions there is a variable in the exponent. It is not numbers (or variables) with constant exponents.

Now express all radicals in exponents.

So the first problem you describe is

\( \huge {\sqrt 8 \over {(\sqrt 8)^5}} = (8^{1 \over 2}) (8^{-{5 \over 2}}) = 8^{-{4 \over 2}} = 8^{-2} = {1 \over {8^2}} \)

Answer 3

Oh, you mean the 5th root, not the 5th power of the square root.

\( \huge (8^{1 \over 2}) (8^{-{1 \over 5}}) = 8^{4 \over {10}} = 8^{2 \over 5}\)

Answer 4

...Yeah, sorry. I didn't mean to type it that way.

Answer 5

No. 1/2 - 1/5 is 3/10. I had that and convinced myself it was wrong.

Answer 6

Also, sorry about the subject being wrong. The unit is on exponential functions. This is the most difficult unit for me, as it combines two of my worst numerical nightmares; radicals, and fractions. COMBINED, mind you.

Answer 7

Can I get help on second one as well, if you can? This one is just completely insane.

Answer 8

\[\Huge \frac{ \sqrt[3]{5} \sqrt{5}}{ \sqrt[3]{5^5}}=\frac{ 5^{1 \over 3}\times 5^1 }{ 5^{5 \over 3} }\]

Answer 9

\[\Huge \frac{ 5^\frac{ 4 }{ 3 } }{ 5^\frac{ 5 }{ 3 } }=5^{\frac{ 4 }{ 3 }-\frac{ 5 }{ 3 }}=5^{-\frac{ 1 }{ 3 }}=\frac{ 1 }{ 5^\frac{ 1 }{ 3 } }=\frac{ 1 }{ \sqrt[3]{5} }\]

Answer 10

Thank you!

Answer 11

Yw.