R K Bansal Solutions for Exercise 1: EXERCISE

Solve $3\left(2^x+1\right)-2^{x+2}+5=0$.

If ${\left(a^m\right)}^n=a^m·a^n$, find the value of $m(n-1)-(n-1)$.

If $m=\sqrt[3]{15}$ and $n=\sqrt[3]{14}$, find the value of $m-n-\frac{1}{m^2+mn+n^2}$.

Evaluate $\frac{2^n\times 6^{m+1}\times {10}^{m-n}\times {15}^{m+n-2}}{4^m\times 3^{2m+n}\times {25}^{m-1}}$

Evaluate ${\left(\frac{x^q}{x^r}\right)}^{\frac{1}{qr}}\times {\left(\frac{x^r}{x^p}\right)}^{\frac{1}{rp}}\times {\left(\frac{x^p}{x^q}\right)}^{\frac{1}{pq}}$.

Prove that $\frac{a^{-1}}{a^{-1}+b^{-1}}+\frac{a^{-1}}{a^{-1}-b^{-1}}=\frac{2b^2}{b^2-a^2}$.

Prove that $\frac{a+b+c}{a^{-1}{b}^{-1}+b^{-1}{c}^{-1}+c^{-1}{a}^{-1}}=abc$.

Evaluate $\frac{4}{(216{)}^{-\frac{2}{3}}}+\frac{1}{(256{)}^{-\frac{3}{4}}}+\frac{2}{(243{)}^{-\frac{1}{5}}}$.