[{(3 to power 5by2*5 to power 3by4)/2to power -5by4}/{16/5 to power 1by4*3 to power 1by2)}]to power 1by5
I cannot interpret all those words. What is "by" supposed to mean?
Is 3 to power 5by2
2*3^5 or (3^5)^2
That is, does by mean multiply by or raise to a new power?
Try using
* for multiply
^ for exponent
() to make it clear what is grouped
Ahhh. I think the "by" means division, right? So why not just use / everywhere? I think you have
[{(3^(5/2) * 5^(3/4)) / 2^(-5/4)}/{(16/5)^(1/4) * 3^(1/2)}]^(1/5)
Take a look at how wolframalpha interprets my version of your input. If I got it wrong, play around with the syntax till the displayed version matches what you want.
http://www.wolframalpha.com/input/?i=[{%283^%285%2F2%29+*+5^%283%2F4%29%29+%2F+2^%28-5%2F4%29}%2F{%2816%2F5%29^%281%2F4%29+*+3^%281%2F2%29}]^%281%2F5%29
To simplify the given expression, follow these steps:
Step 1: Evaluate the numerator:
- Calculate 3 to the power of (5/2), which equals √(3^5), so 3^(5/2) = √(3^5) = √(243) = 9.
- Calculate 5 to the power of (3/4), which equals ∛(5^3), so 5^(3/4) = ∛(5^3) = ∛(125) = 5.
- Divide these two results: 9 / 5 = 9/5.
Step 2: Evaluate the denominator:
- Calculate 2 to the power of (-5/4), which is the reciprocal of 2^(5/4). So, 2^(-5/4) = 1 / ∜(2^5) = 1 / ∜(32) = 1 / 2 = 1/2.
- Calculate 16 / (5 to the power of (1/4)), which is the reciprocal of 16 / 5^(1/4). So, 16/(5^(1/4)) = 16 * ∜(5) = 16 * ∜(5) / 1 = 16 * ∜5.
- Calculate 3 to the power of (1/2), which equals √3.
- Divide these two results: (16 * ∜5) / √3 = (16 * ∜5) / √3.
Step 3: Combine the numerator and denominator:
- Divide the numerator by the denominator: (9/5) / ((16 * ∜5) / √3) = (9/5) * (√3) / (16 * ∜5).
- Simplify further if required.
Step 4: Raise the expression to the power of (1/5):
- Raise the above result to the power of (1/5): [(9/5) * (√3) / (16 * ∜5)]^(1/5).
And that is the final simplified expression.