Division Distributive Property- question: 0.0625 = 1 * (1/2)^{x/5730}

[bfischer]

Why does the x/5730 exponent only apply to the denominator (and not also numerator) in this algebra problem?

I'm having trouble finding this answer so I can explain this to my child.

Thanks!

 

[Dr.Peterson]

Why does the x/5730 exponent only apply to the denominator (and not also numerator) in this algebra problem?

I'm having trouble finding this answer so I can explain this to my child.

Thanks!View attachment 36522

But they have applied the exponent to both: 1, raised to any power, is 1. They saw no need to state that.

 

[bfischer]

But they have applied the exponent to both: 1, raised to any power, is 1. They saw no need to state that.

Thanks.

Not sure how it just disappears from the numerator... not as advanced as you.

 

[bfischer]

But they have applied the exponent to both: 1, raised to any power, is 1. They saw no need to state that.

I get what you're saying about 1 raised to a power is 1... but wanting to show my child how it plays out mathematically in this situation.

Or, maybe there's no good explanation other than just showing the simple proof... 1 raises to 1,2,3.... is always 1.

 

[topsquark]

Thanks.

Not sure how it just disappears from the numerator... not as advanced as you.

[imath]1^n=1[/imath] for any value of n. So
[imath]\left ( \dfrac{1}{2} \right ) ^n = \dfrac{1^n}{2^n} = \dfrac{1}{2^n}[/imath]

-Dan

 

[bfischer]

[imath]1^n=1[/imath] for any value of n. So
[imath]\left ( \dfrac{1}{2} \right ) ^n = \dfrac{1^n}{2^n} = \dfrac{1}{2^n}[/imath]

-Dan

Thanks

 

[bfischer]

[imath]1^n=1[/imath] for any value of n. So
[imath]\left ( \dfrac{1}{2} \right ) ^n = \dfrac{1^n}{2^n} = \dfrac{1}{2^n}[/imath]

-Dan

I was thinking a fractional exponent had some special exception to the rule... mind playing tricks on me!

 

[Steven G]

Consider \(\displaystyle 8^{4/3}\). To calculate this you need to ask yourself what times itself 3 times gives you 8. That answer is 2. Now you need to compute 2⁴ which is 16. In the end \(\displaystyle 8^{4/3}\)=16.

Now we do the same thing with \(\displaystyle 1^{4/3}\). What times itself 3 times gives you 1--answer is 1. Now compute 1⁴. That's 1 as well. So in the end, \(\displaystyle 1^{4/3}\) = 1.

 

[bfischer]

Consider \(\displaystyle 8^{4/3}\). To calculate this you need to ask yourself what times itself 3 times gives you 8. That answer is 2. Now you need to compute 2⁴ which is 16. In the end \(\displaystyle 8^{4/3}\)=16.

Now we do the same thing with \(\displaystyle 1^{4/3}\). What times itself 3 times gives you 1--answer is 1. Now compute 1⁴. That's 1 as well. So in the end, \(\displaystyle 1^{4/3}\) = 1.

Thanks so much... I just connected that when showing my child. A fractional exponent to one always works out to be 1.

Much appreciated

 

[Steven G]

Thanks so much... I just connected that when showing my child. A fractional exponent to one always works out to be 1.

Much appreciated

The real question to ponder is what does \(\displaystyle 1^{\sqrt{2}}\ equal? \)

 

[khansaheb]

The real question to ponder is what does \(\displaystyle 1^{\sqrt{2}}\ equal? \)

[cos(2* π) + i * sin(2 * π)]^√2 = [e^i2π]^√2 = [cos(2√2* π) + i * sin(2√2 * π)]

Real 1^√2 = real{cos(2* π) + i * sin(2 * π)}^√2 → cos(2√2* π)

 

[Steven G]

[cos(2* π) + i * sin(2 * π)]^√2 = [e^i2π]^√2 = [cos(2√2* π) + i * sin(2√2 * π)]

Real 1^√2 = real{cos(2* π) + i * sin(2 * π)}^√2 → cos(2√2* π)

Oh boy, you're going against Dr Peterson who claims that 1 raised to any power, is 1. Watch out!