Answer:
1) The value of [tex]\frac{(8^3)^48^{-9}}{8^3}[/tex] is 1.
2) The value of [tex]\frac{8^38^{4}}{(8^2)^4}[/tex] is [tex]8^{(-1)}[/tex].
Step-by-step explanation:
Given Expressions,
1) [tex]\frac{(8^3)^48^{-9}}{8^3}[/tex] then
Using property of exponents [tex](a^x)^y=a^{xy}[/tex]
[tex]\frac{(8)^{12}8^{-9}}{8^3}[/tex]
Using property of exponents [tex]a^xa^y=a^{x+y}[/tex]
[tex]\frac{(8)^{12-9}}{8^3}[/tex]
[tex]\Rightarrow \frac{(8)^{3}}{8^3}[/tex]
Using property of exponents [tex]\frac{a^x}{a^y}=a^{x-y}[/tex] and [tex]a^0=1[/tex]
[tex]8^{(3-3)}=8^0=1[/tex]
Thus, The value of [tex]\frac{(8^3)^48^{-9}}{8^3}[/tex] is 1.
[tex]\frac{(8^3)^48^{-9}}{8^3}[/tex]
2) [tex]\frac{8^38^{4}}{(8^2)^4}[/tex]
Now applying property of exponents [tex](a^x)^y=a^{xy}[/tex] in denominator,
[tex]\frac{8^{3}8^{4}}{8^8}[/tex]
Using property of exponents [tex]a^xa^y=a^{x+y}[/tex]
[tex]\frac{8^{3+4}}{8^8}[/tex]
[tex]\Rightarrow \frac{8^{7}}{8^8}[/tex]
Using property of exponents [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]8^{(7-8)}=8^{(-1)}[/tex]
Thus, the value of [tex]\frac{8^38^{4}}{(8^2)^4}[/tex] is [tex]8^{(-1)}[/tex]
