# How to simplify this arithmetic expression

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.

• 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. – user146269 Jan 27 '15 at 3:55

$$(\frac{3}{4})^6 = \frac{3^6}{4^6}$$
$[(3/4)^{7-4}]^2 \times 4^5 = [(3/4)^3]^2 \times 4^5 = (3/4)^6 \times 4^5 = (3^6)/(4^6) \times 4^5 = (3^6)/4 = 729/4$