$$(5\times5 \times5 \times 5 \times 5 \times 5)^{2}$$ x $$(5 \times 5 \times 5 \times 5 )^{8}$$ ÷ $$(5\times5)^{3}$$ = $$25^?$$

The question is $$(5\times5 \times5 \times 5 \times 5 \times 5)^{2}$$ x $$(5 \times 5 \times 5 \times 5 )^{8}$$ ÷ $$(5\times5)^{3}$$ = $$25^?$$

When power of a base is raised to another power the resultant power of the base is the product of the individual powers.

Hence $$(5\times5 \times5 \times 5 \times 5 \times 5)^{2} = 5^{12}$$ , $$(5 \times 5 \times 5 \times 5 )^{8} = 5^{32}$$ and $$(5 \times 5)^{3} = 5^{6}$$

When two numbers of the same base and different powers are multiplied the powers get added.

Hence $$5^{12} \times 5^{32}$$ = $$5^{44}$$.

$$5^{44} = 25^{22}$$ and $$ 5^{6}$$ = $$25^{3}$$

Let the unknown power be a.

$$\frac{25^{22}} {25^{3}}$$ = $$25^{a}$$

Removing the common factor of $$25^ {3}$$ we get,

$$25^{19} =25^{a}$$

a=19.

Hence Option E is the correct answer.