Question

3

Answer 1

Answer:

Option 1 is correct i.e.

$(\frac{2^3\:\textbf{.}\:3^0}{5})^2=\frac{2^6.1^2}{5^2}=\frac{64}{25}$

Step-by-step explanation:

We need to simplify the expression: $(\frac{2^3\:\textbf{.}\:3^0}{5})^2$

We know that: $(a^m)^n= a^{m*n}$ and $a^0=1$

We would use these exponent laws to solve our question.

First we will apply $a^0=1$

$(\frac{2^3\:\textbf{.}\:3^0}{5})^2\\=(\frac{2^3\:\textbf{.}\:1}{5})^2$

Now, we will apply $(a^m)^n= a^{m*n}$

$=\frac{(2^3)^2\:\textbf{.}\:1^2}{5^2}\\=\frac{2^6\:\textbf{.}\:1}{5^2}\\=\frac{64}{25}$

So, the result is: $\frac{64}{25}$

Therefore, Option 1 is correct i.e.

$(\frac{2^3\:\textbf{.}\:3^0}{5})^2=\frac{2^6.1^2}{5^2}=\frac{64}{25}$