Answer:
(a) [tex]4^7[/tex]
(b) [tex]7^6[/tex]
(c) [tex]\dfrac{1}{16}[/tex]
(d) [tex]3^{4}[/tex]
Step-by-step explanation:
We need to simplify the given expressions.
(a)
Consider the given expression is
[tex](4^5)(4^2)[/tex]
Using the property of exponent, we get
[tex]=4^{5+2}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]=4^7[/tex]
(b)
Consider the given expression is
[tex](7^2)^3[/tex]
Using the property of exponent, we get
[tex]=7^{2\times 3}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]=7^6[/tex]
(c)
Consider the given expression is
[tex]2^{-4}[/tex]
Using the property of exponent, we get
[tex]=\dfrac{1}{2^{4}}[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
[tex]=\dfrac{1}{16}[/tex]
(d)
Consider the given expression is
[tex]\dfrac{3^8}{3^4}[/tex]
Using the property of exponent, we get
[tex]=3^{8-4}[/tex] [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]
[tex]=3^{4}[/tex]
