Answer:
Option 1 is correct i.e.
[tex](\frac{2^3\:\textbf{.}\:3^0}{5})^2=\frac{2^6.1^2}{5^2}=\frac{64}{25}[/tex]
Step-by-step explanation:
We need to simplify the expression: [tex](\frac{2^3\:\textbf{.}\:3^0}{5})^2[/tex]
We know that: [tex](a^m)^n= a^{m*n}[/tex] and [tex]a^0=1[/tex]
We would use these exponent laws to solve our question.
First we will apply [tex]a^0=1[/tex]
[tex](\frac{2^3\:\textbf{.}\:3^0}{5})^2\\=(\frac{2^3\:\textbf{.}\:1}{5})^2\\[/tex]
Now, we will apply [tex](a^m)^n= a^{m*n}[/tex]
[tex]=\frac{(2^3)^2\:\textbf{.}\:1^2}{5^2}\\=\frac{2^6\:\textbf{.}\:1}{5^2}\\=\frac{64}{25}[/tex]
So, the result is: [tex]\frac{64}{25}[/tex]
Therefore, Option 1 is correct i.e.
[tex](\frac{2^3\:\textbf{.}\:3^0}{5})^2=\frac{2^6.1^2}{5^2}=\frac{64}{25}[/tex]
