Answer
See Laws below
Work Step by Step
$$ a^n*a^w=a^{n+w}$$ $$ 5^2*5^5=5^{7}$$
$$ a^n/a^m = a^{n-m} $$ $$ 5^2/5^1 = 5^{1} $$
$$ ({a^n})^d={a^n}^d$$ $$ ({2^3})^7=2^{21}$$
$$ (ay)^w=a^w*y^w$$ $$ (2*3)^2=2^2*3^2$$
$$ (\frac{a}{b})^n=a^n/(b^n) $$ $$ (\frac{2}{3})^3=2^3/(3^3) $$
