Use the power law $a^x\cdot a^y=a^{x+y}a^x\; \backslash cdot\; a^y\; =\; a^\{x+y\}$ with $x=2,y=1,a=3x=2,\; y=1,\; a=3$.

Conclude the exponent.

First apply the power laws to $4^2\cdot 4^{9}4^2\; \backslash cdot\; 4^9$.

Now apply the power law to $4^{11}\cdot 4^{-12}4^\{11\}\; \backslash cdot\; 4^\{-12\}$.

The term can be simplified even further by using the rule of the negative exponent, that is $a^{-1}=\frac{1}{a}\mathrm{.}a^\{-1\}=\backslash frac\{1\}\{a\}.$

Apply the power law $a^x\cdot a^y=a^{x+y}a^\{x\}\; \backslash cdot\; a^y\; =\; a^\{x\; +y\}$ to $2^{-3}\cdot 2^{5}2^\{-3\}\; \backslash cdot\; 2^5$.

Write $2^2=2\cdot 2=4=4^{1}2^2=2\backslash cdot2=4=4^1$.

Apply the power law $a^x\cdot a^y=a^{x+y}a^\{x\}\; \backslash cdot\; a^y\; =\; a^\{x\; +y\}$ to $4^8\cdot 4^{1}4^8\; \backslash cdot\; 4^1$.

Apply the power law $a^x\cdot b^x=(a\cdot b{)}^{x}a^x\; \backslash cdot\; b^x\; =\; (a\backslash cdot\; b)^x$.

Apply the power law ${\left(a^x\right)}^y=a^{x\cdot y}\backslash left(a^x\; \backslash right)^y=a^\{x\backslash cdot\; y\}$.

Conclude the exponent

Apply the power law $\frac{a^x}{a^y}=a^{x-y}\backslash frac\{a^x\}\{a^y\}=a^\{x-y\}$ to $\frac{9^2}{9^{-3}}\backslash frac\{9^2\}\{9^\{-3\}\}$.

Summarize the exponent of $99$.

Write $a:b=\frac{a}{b}a:b=\backslash frac\{a\}\{b\}$.

Use the power law $\frac{a^x}{b^x}={\left(\frac{a}{b}\right)}^x\backslash frac\{a^x\}\{b^x\}=\backslash left(\; \backslash frac\; \{a\}\{b\}\; \backslash right)^x$.

Conclude the base.

Use the power law $\frac{a^x}{a^y}=a^{x-y}\backslash frac\{a^x\}\{a^y\}=a^\{x-y\}$ with base $a=26a=26$.

Use the power law $\frac{a^x}{a^y}=a^{x-y}\backslash frac\{a^x\}\{a^y\}=a^\{x-y\}$ with base $a=13a=13$.

Use the power law $\frac{a^x}{b^x}={\left(\frac{a}{b}\right)}^x\backslash frac\{a^x\}\{b^x\}=\backslash left(\; \backslash frac\{a\}\{b\} \backslash right)^x$.

Conclude the base.