Answer:
Step-by-step explanation:
[tex]75^{30}\\\\75=3\cdot5\cdot5=3\cdot5^2\\\\75^{30}=(3\cdot5^2)^{30}=3^{30}\cdot(5^2)^{30}=3^{30}\cdot5^{60}[/tex]
[tex]45^{45}\cdot15^{15}\\\\45=3\cdot3\cdot5=3^2\cdot5\\15=3\cdot5\\\\45^{45}=(3^2\cdot5)^{45}=(3^2)^{45}\cdot5^{45}=3^{90}\cdot5^{45}\\15^{15}=(3\cdot5)^{15}=3^{15}\cdot5^{15}\\\\45^{45}\cdot15^{15}=3^{90}\cdot5^{45}\cdot3^{15}\cdot5^{15}=3^{90+15}\cdot5^{45+15}=3^{105}\cdot5^{60}\\\\=3^{75+30}\cdot5^{60}=3^{75}\cdot\underbrace{3^{30}\cdot5^{60}}_{75^{30}}=3^{75}\cdot75^{30}[/tex]
[tex]\text{therefore it is divisible by}\ 75^{30}[/tex]
[tex]Used:\\\\(ab)^n=a^nb^m\\\\(a^n)^m=a^{nm}\\\\a^n\cdot a^m=a^{n+m}[/tex]
