Answer
The statement does not make sense.
$25(x^{3})^{9} \ne25x^{12}$
Work Step by Step
To determine whether or not the statement makes sense, evaluate all the given equations.
1. $(5x^{6})^{2}$
Products to Powers rule: $(ab)^{n} = a^{n}\cdot b^{n}$
Thus,
$$(5x^{6})^{2}$$ $$= (5^{2}x^{6\cdot 2})$$ $$=25x^{12}$$
2. $(5x^{3})(5x^{9})$
Recall the product rule: $a^{m}⋅a^{n}=a^{m+n}$
Thus,
$$(5x^{3})(5x^{9})$$ $$=25x^({3+9})$$ $$=25x^{12}$$
3. $25(x^{3})^{9}$
Recall the power rule: $(a^{m})^{n}=a^{mn}$
Thus,
$$25(x^{3})^{9}$$ $$=25x^{(3\cdot 9)}$$ $$=25x^{27}$$
4. $5^{2}(x^{2})^{6}$
Using the power rule,
$$5^{2}(x^{2})^{6}$$ $$=25x^{(2\cdot 6)}$$ $$=25x^{12}$$
Since not all the given expressions are equal to $25x^{12}$, therefore the statement does not make sense.
