Respuesta :
Answer:
(a) [tex]5^{8}[/tex]
(b) 3
(c) 27
(d) [tex]\dfrac{1}{6}[/tex]
Step-by-step explanation:
We need simplify the given expressions.
(a)
Consider the given expression is
[tex](5^4)(25^2)[/tex]
[tex](5^4)((5^2)^2)[/tex]
Using the properties of exponents we get
[tex](5^4)(5^4)[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]5^{4+4}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]5^{8}[/tex]
(b)
Consider the given expression is
[tex](9^{\frac{1}{3}})(3^{\frac{1}{3}})[/tex]
[tex]((3^2)^{\frac{1}{3}})(3^{\frac{1}{3}})[/tex]
Using the properties of exponents we get
[tex](3^{\frac{2}{3}})(3^{\frac{1}{3}})[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]3^{\frac{2}{3}+\frac{1}{3}}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]3^{1}[/tex]
[tex]3[/tex]
(c)
Consider the given expression is
[tex](\dfrac{1}{3})^{-3}[/tex]
Using the properties of exponents we get
[tex](\dfrac{3}{1})^{3}[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
[tex]3^{3}[/tex]
[tex]27[/tex]
(d)
Consider the given expression is
[tex](6^4)(6^{-5})[/tex]
Using the properties of exponents we get
[tex]6^{4+(-5)}[/tex] [tex][\because a^ma^n=a^{m+n}][/tex]
[tex]6^{-1}[/tex]
[tex]\dfrac{1}{6^{1}}[/tex] [tex][\because a^{-n}=\dfrac{1}{a^n}][/tex]
[tex]\dfrac{1}{6}[/tex]
