a) \(125\cdot5^2\cdot\dfrac{1}{625}\cdot5^3\)
\(=5^3\cdot5^2\cdot\dfrac{1}{625}\cdot5^3\)
\(=5^8\cdot\dfrac{1}{5^4}\)
\(=\dfrac{5^8}{5^4}\)
\(=5^4=625\)
b) \(8\cdot32\cdot\left(2^4\cdot\dfrac{1}{32}\right)\)
\(=2^3\cdot2^5\cdot\left(2^4\cdot\dfrac{1}{2^5}\right)\)
\(=2^3\cdot2^5\cdot\dfrac{2^4}{2^5}\)
\(=2^8:\dfrac{1}{2}\)
\(=2^8\cdot2\)
\(=2^9=512\)
c) \(6^3\cdot5^2\cdot\left(\dfrac{5}{6}\right)^3\)
\(=6^3\cdot5^2\cdot\dfrac{125}{216}\)
\(=\dfrac{6^3\cdot5^2\cdot5^3}{6^3}\)
\(=5^2\cdot5^3=5^5\)
a: =5^3*5^3*5^2*1/5^4=5^4
b: =2^3*2^5:1/2
=2^8*2=2^9
c: =6^3*5^2*5^3*/6^3=5^5
