Answer: a) 15625, b) 0.2, c) 625, d) 0.008.
Step-by-step explanation:
Since we have given that
a) [tex](5^2)(5^3)[/tex]
As we know that
[tex]a^m\times a^n=a^{m+n}[/tex]
So, it becomes,
[tex]5^2\times 5^3=5^{2+3}=5^6=15625[/tex]
(b) [tex](5^2)(5^{-3})[/tex]
So, it becomes,
[tex]5^2\times 5^{-3}=5^{2-3}=5^{-1}=\dfrac{1}{5}=0.2[/tex]
(c) [tex](5^2)^2[/tex]
As we know that
[tex](a^m)^n=a^{mn}[/tex]
So, it becomes,
[tex]5^{2\times 2}=5^4=625[/tex]
(d) [tex]5^{-3}[/tex]
[tex]a^{-m}=\dfrac{1}{a^m}\\\\5^{-3}=\dfrac{1}{5^3}=\dfrac{1}{125}=0.008[/tex]
Hence, a) 15625, b) 0.2, c) 625, d) 0.008.
