What is $\frac{1}{(-7^{3})^{3}}\cdot(-7)^{10}$?
I notice that this expression involves powers of negative seven, so I can try to simplify it using the rules of exponents. First, I see that there is a fraction with a power of negative seven in the denominator. I can use the rule that $\frac{1}{a^n}=a^{-n}$ to rewrite this as $(-7^{3})^{-3}\cdot(-7)^{10}$. Next, I see that there is a power of a power in the first term. I can use the rule that $(a^m)^n=a^{mn}$ to rewrite this as $(-7)^{-9}\cdot(-7)^{10}$. Now, I have two terms with the same base of negative seven, but different exponents. I can use the rule that $a^m\cdot a^n=a^{m+n}$ to combine them into one term as $(-7)^{1}$. Finally, I see that this is just equal to negative seven, so I have my answer. 