If \(\frac{({a^2b^{-3}c})^{3/4}}{a^{-1}b^4c^5}\) = \(a^p b^q c^r\); what is the value of p+2q?

If 314\(_{10}\) - 256\(_7\) = 340\(_x\), find x.

Simplify \(\frac{3(2^{n+1}) - 4(2^{n-1})}{2^{n+1} - 2^n}\)

Evaluate \(Log_{\sqrt{2}}4 + Log_{\frac{1}{2}}16 - Log_{4}32\)

simplify \(16^{\frac{-1}{2}}\times 4^{\frac{-1}{2}} \times 27^{\frac{1}{3}}\)