Simplify. Assume all variables represent positive real numbers.
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Question

Quizplus · Accepted Answer

There are no like terms to combine, so we simply add the exponents of each variable.

11ebb63d_1bfd_a4eb_b851_ff56550900a6_TB8475_11 = 1e^11 * 1b * 1c^6 * 3d * 1d^2 * 1a^4 * 1f^5 * 1f^5 * 5b * 1T * 1B^8

= 1e^11 * 1a^4 * 1b * 6c^6 * 4d * 25f^5 * 5b * 1T * 1B^8

= 11ebb63d_1bfd_a4ee_b851_99905caf11a4_TB8475_11 (by adding the exponents)

Therefore, the answer is (C). When we simplify the given expression, we can use the fact that $$a^{bc}=(a^b)^c.$$ Applying this rule to the given expression, we have \begin{align*}
\sqrt{e^{2\ln 2}}\cdot \sqrt[3]{e^{3\ln 3}}\cdot \sqrt[4]{e^{4\ln 4}} &= \sqrt{(2^2)^{\ln2}}\cdot \sqrt[3]{(3^3)^{\ln 3}}\cdot \sqrt[4]{(4^4)^{\ln 4}}\
&= \sqrt{(2^{\ln2})^2}\cdot \sqrt[3]{(3^{\ln 3})^3}\cdot \sqrt[4]{(4^{\ln4})^4}\
&= 2^{(\ln2)^2}\cdot 3^{(\ln3)^3}\cdot 4^{(\ln4)^4}.
\end{align*}
Therefore, the answer is $\boxed{	extbf{(C) }11ebb63d\_1bfd\_a4ee\_b851\_99905caf11a4\_TB8475\_11}$.

Simplify. Assume All Variables Represent Positive Real Numbers