Answer: a) [tex]\dfrac{1}{5}[/tex] b) 27 c) 5 d) [tex]2^{12}=4096[/tex]
Step-by-step explanation:
Properties of exponent :
By using above properties we simplify the given expressions.
a) [tex]\dfrac{5^3}{25^2}=\dfrac{5^3}{(5^2)^2}[/tex]
[tex]=\dfrac{5^3}{5^4}[/tex] [ By using (3)]
[tex]=5^{3-4}=5^{-1}[/tex] [ By using (2)]
[tex]=\dfrac{1}{5}[/tex] [ By using (4)]
b) [tex](9^{\frac{2}{3}})(3)(3^{\frac{3}{2}})[/tex]
[tex]=((3^{2})^{\frac{2}{3}})(3^{1+\frac{3}{2}})[/tex] [ By using (1)]
[tex]=(3^{\frac{4}{3}})(3^{\frac{5}{2}})[/tex] [ By using (3)]
[tex]=3^{\frac{4}{3}+\frac{5}{3}}[/tex] [ By using (1)]
[tex]=3^{\frac{4+5}{3}}=3^{\frac{9}{3}=3^3=27}[/tex]
c) [tex][(25)^\frac{1}{2}(5^2)]^{\frac{1}{3}} =[(5^2)^\frac{1}{2}(5^2)]^\frac{1}{3}[/tex]
[tex]=[(5)(5^2)]^\frac{1}{3}[/tex] [ By using (3)]
[tex]=[5^{1+2}]^\frac{1}{3}[/tex] [ By using (1)]
[tex]=5^{3\times\frac{1}{3}})= 5[/tex] [ By using (3)]
d) [tex](8^2)(4^3)= (2^3)^2((2^2)^3)[/tex] [ By using (5)]
[tex]=(2^6)(2^6)[/tex] [ By using (3)]
[tex]=2^{6+6}=2^{12}=4096[/tex]
