k) \(125^5:25^3\)
\(=\left(5^3\right)^5:\left(5^2\right)^3\)
\(=5^{15}:5^6\)
\(=5^{15-6}\)
\(=5^9\)
l) \(27^6:9^3\)
\(=\left(3^3\right)^6:\left(3^2\right)^3\)
\(=3^{18}:3^6\)
\(=3^{18-6}\)
\(=3^{12}\)
m) \(4^{20}:2^{15}\)
\(=\left(2^2\right)^{20}:2^{15}\)
\(=2^{40}:2^{15}\)
\(=2^{40-15}\)
\(=2^{25}\)
n) \(24^n:2^{2n}\)
\(=6^n\cdot4^n:\left(2^2\right)^n\)
\(=6^n\cdot4^n:4^n\)
\(=6^n\)
p) \(64^4\cdot16^5:4^{20}\)
\(=\left(4^3\right)^4\cdot\left(4^2\right)^5:4^{20}\)
\(=4^{12}\cdot4^{10}:4^{20}\)
\(=4^{12+10-20}\)
\(=4^2\)
q) \(32^4:8^6\)
\(=\left(2^5\right)^4:\left(2^3\right)^6\)
\(=2^{20}:2^{18}\)
\(=2^{20-18}\)
\(=2^2\)
k: =(5^3)^5:(5^2)^3
=5^15:5^6=5^9
l: =(3^3)^6:(3^2)^3
=3^18:3^6=3^12
m: =2^40:2^15=2^25
n: \(=\dfrac{24^n}{4^n}=6^n\)
p: \(=\left(4^3\right)^4\cdot\dfrac{\left(4^2\right)^5}{4^{20}}=\dfrac{4^{12}\cdot4^{10}}{4^{20}}=4^2\)
q: \(=\left(2^5\right)^4:\left(2^3\right)^6=\dfrac{2^{20}}{2^{18}}=2^2\)
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