The difference between expanding and index laws?

Would you mind explaining 'b' in a little bit more detail? as in how you got that answer?

a. Show, by expanding, that 3¹⁰=9⁵

b. Show, using index laws, that 3¹⁰=9⁵

Don't they just mean the same thing?

I assume

a.

$\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3\cdot 3 &=& 9\cdot 9\cdot 9\cdot 9\cdot 9 \\ 59049 &=& 59049 \end{array}$

b.

$\begin{array}{rcll} 3^{10} &=& 9^5 \\ 3^{2\cdot 5} &=& 9^5 \\ (3^2)^5 &=& 9^5 \\ 9^5 &=& 9^5 \\ \end{array}$

Thank you so much! That makes a bit more sense now :)