Indices

Question 40

If ${{2}^{x+y}}=16$ and ${{4}^{x-y}}=\frac{1}{32}$ , find the values of x and y

Simplify ${{81}^{\tfrac{-3}{4}}}\times {{25}^{\tfrac{1}{2}}}\times {{243}^{\tfrac{2}{5}}}$

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

Evaluate $\frac{{{5}^{-3}}\times {{5}^{-4}}}{{{5}^{-6}}\times {{5}^{-2}}}$

If $\frac{{{4}^{x+3}}}{{{16}^{2x-3}}}=1$ find x

Solve for x in $8{{x}^{-2}}=\frac{2}{25}$

$\text{Simplify }\frac{{{3}^{-5n}}}{{{9}^{1-n}}}\times {{27}^{n+1}}$

If ${{27}^{x+2}}\div {{9}^{x+1}}={{3}^{2x}}$, find x

Simplify ${{\left( \frac{16}{81} \right)}^{\tfrac{1}{4}}}\div {{\left( \frac{9}{16} \right)}^{-\tfrac{1}{2}}}$

Evaluate ${{\left( \frac{81}{16} \right)}^{-\tfrac{1}{4}}}\times {{2}^{-1}}$