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I'm trying to simplify:

$\left[(\frac{3}{4}\right)^{7}\cdot$ $\left(\frac{3}{4}\right)^{-4}]^{2}$ $\cdot4^5$

The only advance that I have done is

$\left[(\frac{3}{4}\right)^{14}\cdot$ $\left(\frac{3}{4}\right)^{-8}]$ $\cdot4^5$ and then $\left[(\frac{3}{4}\right)^{6}]$ $\cdot4^5$

the answer is$$\frac{3^6}{4}=\frac{729}{4}$$

I do not know what to do next, can someone please guide me in how to solve this exercise.

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  • $\begingroup$ Yes this is indeed the right answer. Start from the inside then work your way to the outside. Inside try to imply the exponential rule $a^n \times a^m = a^ {m+n}$ then use the power rule $(a^n)^m = a^{mn}$ then simplify. $\endgroup$ – user146269 Jan 27 '15 at 3:55
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Hint:

$$(\frac{3}{4})^6 = \frac{3^6}{4^6} $$

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  • $\begingroup$ Ok I understand now the 4 is now 4 ^ -1 so it is 1/4, sorry if my question is very basic I am not good at math $\endgroup$ – Learner Jan 27 '15 at 3:35
  • $\begingroup$ You simply have not had the same experiences as others to enrich your mathematics. There is no question that is too basic, as long as you have made the effort to first think for yourself. $\endgroup$ – Chantry Cargill Jan 27 '15 at 3:37
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    $\begingroup$ Ok thanks for answering $\endgroup$ – Learner Jan 27 '15 at 3:39
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$[(3/4)^{7-4}]^2 \times 4^5 = [(3/4)^3]^2 \times 4^5 = (3/4)^6 \times 4^5 = (3^6)/(4^6) \times 4^5 = (3^6)/4 = 729/4$

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