<ol class="abc-list"><li><div class="list-item-paragraph">Simplify $\frac{{{4}^{x+2}}-{{2}^{2x+1}}}{{{8}^{x}}\left( {{4}^{1-x}} \right)}$ and express it in the form $a\left( {{2}^{x-b}} \right)$ where $a$ and $b$ are integers.<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">Hence, solve for $x$ if $\frac{{{4}^{x+2}}-{{2}^{2x+1}}}{{{8}^{x}}\left( {{4}^{1-x}} \right)}=15$.<span class="inline-marks">[2]</span></div></li></ol>

Simplify $\frac{{{4}^{x+2}}-{{2}^{2x+1}}}{{{8}^{x}}\left( {{4}^{1-x}} \right)}$ and express it in the form $a\left( {{2}^{x-b}} \right)$ where $a$ and $b$ are integers.

Hence, solve for $x$ if $\frac{{{4}^{x+2}}-{{2}^{2x+1}}}{{{8}^{x}}\left( {{4}^{1-x}} \right)}=15$.

Techniques of Differentiation - Differentiation of Trigonometric, Logarithmic and Exponential Functions - General

Techniques of Differentiation - Differentiation of Trigonometric, Logarithmic and Exponential Functions - General