Thread: [SOLVED] Fractional Exponents

Can someone please help me solve

81^3/4
__

16

Hopefully this displays correctly. In case it doesn't here it is again:
(81 / 16)^(3 / 4)

I can solve it with the calculator obviously (3 3/8), but I need to demonstrate it and I can't figure out how.

Thank you so much for your help!

Neenoon

If x is positive, p and q are integers where q is positive then,
x^(p/q)= q root of (x^p).

So (81/16)^(3/4) = 4 root of [ (81/16)^(3) ] = 27/8 or 3 3/8.

Hello, Neenoon!

Simplify: .(81/16)^{¾}

We have: .(81)^{¾} / (16)^{¾}

Since .81 = 3^4 .and .16 = 2^4,

. . we have: .(3^4)^{¾} / (2^4)^{¾} .= .(3^3) / (2^3) .= .27/8

I understand the demonstration. Thank you both so much, this prooves very useful.