Question 1183522
Calculate: (-2/3*2%)^4*(-3/4*3%)^3*(-4/5*4%)^2*(-5/6*5%)*10^20 

I’ve been trying to find a sleek way to solve this problem for a long time, but I can’t think of any other way than to just solve it with brute force. Any help would be appreciated, thank you!
<pre>{{{((- 2/3) * "2%")^4 * ((- 3/4) * "3%")^3*((- 4/5) * "4%")^2*((- 5/6) * "5%") * 10^20}}}
{{{((- 2/3) * (2/100))^4 * ((- 3/4) * (3/100))^3*((- 4/5) * (4/100))^2 * ((- 5/6) * (5/100)) * 10^20}}}
{{{(- 4/3(100))^4 * (- 9/4(100))^3 * (- 16/5(100))^2 * (- 25/6(100)) * 10^20}}}
{{{(- 4/3(10^2))^4 * (- 9/4(10^2))^3 * (- 16/5(10^2))^2 * (- 25/6(10^2)) * 10^20}}}
{{{(4^4/(3^4 * (10^2)^4)) * (- 9^3/(4^3 * (10^2)^3)) * (16^2/(5^2 *(10^2)^2)) * (- 5^2/6(10^2)) * 10^20}}}
{{{(4^4/(3^4 * (10^8))) * (- 9^3/(4^3 * (10^6))) * (16^2/(5^2 *(10^4))) * (- 5^2/6(10^2)) * 10^20}}}
{{{(4^4/3^4) * (1/(10^8)) * (- 9^3/4^3) * (1/(10^6)) * (16^2/5^2) * (1/(10^4)) * (- 5^2/6) * (1/(10^2)) * 10^20}}}
{{{(4^4/3^4) * (- 9^3/4^3) * (16^2/5^2) * (- 5^2/6) * (1/(10^8)) * (1/(10^6)) * (1/(10^4)) * (1/(10^2)) * 10^20}}}
{{{(4^4/3^4) * (- 9^3/4^3) * (16^2/5^2) * (- 5^2/6) * (1/(10^(8 + 6 + 4 + 2))) * 10^20}}}
{{{(4^4/3^4) * (- 9^3/4^3) * (16^2/5^2) * (- 5^2/6) * (1/10^20) * 10^20}}}
{{{(4^4/3^4) * (- 9^3/4^3) * (16^2/5^2) * (- 5^2/6) * (1/cross(10^20)) * 10^cross(20)}}}
{{{(4^4/3^4) * (- 9^3/4^3) * (16^2/5^2) * (- 5^2/6)}}}
{{{(4^4/3^4) * (- (3^2)^3/4^3) * (16^2/5^2) * (- 5^2/6)}}}
{{{(4^4/3^4) * (- 3^6/4^3) * (16^2/5^2) * (- 5^2/6)}}}
{{{(4cross(4^4)/3^4) * (- 3^6/cross(4^3)) * (16^2/5^2) * (- 5^2/6)}}} ----- Cancelling base 4 in numerator and denominator
{{{(4/cross(3^4)) * (- 3^2cross(3^6)/1) * (16^2/5^2) * (- 5^2/6)}}} ----- Cancelling base 3 in numerator and denominator
{{{(4/1) * (- 3^2/1) * (16^2/cross(5^2)) * (- cross(5^2)/6)}}} ----- Cancelling base 5 in numerator and denominator
{{{(2cross(4)/1) * (- 3^2/1) * (16^2/1) * (- 1/3cross(6))}}} ----- Cancelling 4 and 6 in numerator and denominator
{{{(2/1) * (- 3cross(3^2)/1) * (16^2/1) * (- 1/1cross(3))}}} ----- Cancelling 3 in numerator and denominator
{{{highlight_green(matrix(1,3, 2(- 3)(16^2)(- 1), "=", "1,536"))}}} <====== Final Answer</pre>