To solve this problem, use rules for exponents such as shown below:
a^-n=1/a^n=1^n/a^n=(1/a)^n (a≠0), a^mn=(a^m)^n, and a^m/b^m=(a/b)^m (b≠0), where a,b,m,n are any real numbers with the limitations listed. Each term of the given equations can be written as follows:
10 to the negative one-third: 10^(-1/3)=1/10^(1/3)=(1/10)^(1/3), 25 to the two-thirds: 25^(2/3)=(25^2)^(1/3)=625^(1/3), and 2 to the five-thirds: 2^(5/3)=(2^5)^(1/3)=32^(1/3)
Thus, this problem can be solved as follows:
10^(-1/3) x 25^(2/3) ÷ 2^(5/3) = (1/10)^(1/3) x 625^(1/3) ÷ 32^(1/3) = (1/10 x 625 ÷ 32)^(1/3)
= (625/(10x32))^(1/3) = (125/64)^(1/3) = (5^3/4^3)^(1/3) = ((5/4)^3)^(1/3) = (5/4)^(3x1/3) = (5/4)
Therefore, the answer is: 10^(1/3) x 25^(2/3) ÷ 2^(5/3) = 5/4 (=1.25)