Answer:
Step-by-step explanation:
[tex]a^{m}*a^{n}=a^{m+n}\\\\\frac{a^{m}}{a^{n}}=a^{m-n}\\\\(a^{m})^{n}=a^{m*n}\\\\a) 3^{5}*3^{x} = 3^{3}*9=3^{3}*3^{2}\\\\ 3^{5+x} =3^{3+2}[/tex]
Compare the exponents,
5 +x = 5
x = 5-5
x = 0
[tex]b) \frac{4^{x}*4^{8}}{4^{2}}=(4^{7})^{1}\\\\4^{x+8-2}=4^{7*1}\\4^{x + 6}=4^{7}[/tex]
Compare the exponents,
x +6 = 7
x = 7-6
x = 1
[tex]c)\frac{a^{8}*a^{5}}{a^{2}}=\frac{a^{x}}{a^{2}}\\\\a^{8+5-2}=a^{x-2}\\\\a^{11}=a^{x-2}[/tex]
Compare the exponents,
x - 2 = 11
x = 11+2
x = 13
[tex]d)\frac{(5^{3})^{x}}{5^{6}}=5^{10}*5^{8}\\\\5^{3x-6}=5^{10+8}\\\\5^{3x-6}=5^{18}[/tex]
Compare the exponents,
3x -6= 18
3x = 18 + 6
3x = 24
x = 24/3
x = 8
