Multiply and simplify

Soroban · **Posted:** Sat, 14 Jan 2012 20:19:32 UTC

Nokia12 wrote:

$\text{1. Simplify: }\:\;\;64^4\cdot 125^8\cdot 100^{12}=?$

. . $A)\;10^{18}\quad B)\;10^{24}\quad C)\;10^{36}\quad D)\;10^{48}$

$\text{I used calculator so the result is:}\;\;10^{48}$

$\text{But how can I simplify? Thanks}$

Note that: . $\begin{Bmatrix}64^4 &=& (2^6)^4 &=& 2^{24} \\ 125^8 &=& (5^3)^8 &=& 5^{24} \\ 100^{12} &=& (2^2\!\cdot\!5^2)^{12} &=& 2^{24}\!\cdot\!5^{24} \end{Bmatrix}$

The problem becomes: . $(2^{24})\cdot(5^{24})\cdot(2^{24}\cdot5^{24} )\;=\;2^{48}\cdot5^{48} \;=\;(2\cdot5)^{48} \;=\;10^{48}$

Nokia12 · **Joined:** Sat, 14 Jan 2012 09:34:25 UTC **Posts:** 4

Thank you very much.

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Multiply and simplify

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