$$\left\{\left[\left(\frac29\right)^4\times\left(\frac3{14}\right)^4\right]^4:\left[\left(-\frac17\right)^2\right]\right\}\times\left[\left(-\frac56\right)^3:\left(\frac5{18}\right)^3\right]^3$$
I've been trying to simplify this expression for $3$ hours. I've tried all the properties of the powers I know, and I've tried many calculators online. The result should be $-3$, but the calculators (at least the ones I've tried) and I can not calculate this expression getting the right result.
I understand it's a very simple thing, but I'm losing my mind...
Given the exponents, the global sign is negative.
Proceed by simplifications of the fractions (keeping an eye on the exponents).
$$\left\{\left[\left(\frac29\right)^4\times\left(\frac3{14}\right)^4\right]^4:\left[\left(\frac17\right)^2\right]\right\}\times\left[\left(\frac56\right)^3:\left(\frac5{18}\right)^3\right]^3$$
$$=\left\{\left[\left(\frac13\right)^4\times\left(\frac1{7}\right)^4\right]^4:\left[\left(\frac17\right)^2\right]\right\}\times\left[\left(\frac11\right)^3:\left(\frac1{3}\right)^3\right]^3$$
$$=\left\{\left[\left(\frac13\right)^{16}\times\left(\frac1{7}\right)^{16}\right]:\left[\left(\frac17\right)^2\right]\right\}\times\left[1:\left(\frac1{3}\right)\right]^9$$
$$=\left\{\left[\left(\frac13\right)^{7}\times\left(\frac1{7}\right)^{14}\right]\right\}.$$
Finally,
$$-\frac1{3^77^{14}}=-\frac1{1483273860320763}.$$