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\frac{5^{2}\left(-4\right)^{3}\left(-4\right)^{12}\times 5^{3}}{\left(5^{2}\right)^{2}\left(-4\right)^{4}\left(-4\right)^{8}}
To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.
\frac{5^{5}\left(-4\right)^{3}\left(-4\right)^{12}}{\left(5^{2}\right)^{2}\left(-4\right)^{4}\left(-4\right)^{8}}
To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.
\frac{5^{5}\left(-4\right)^{15}}{\left(5^{2}\right)^{2}\left(-4\right)^{4}\left(-4\right)^{8}}
To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.
\frac{5^{5}\left(-4\right)^{15}}{5^{4}\left(-4\right)^{4}\left(-4\right)^{8}}
To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.
\frac{5^{5}\left(-4\right)^{15}}{5^{4}\left(-4\right)^{12}}
To multiply powers of the same base, add their exponents. Add 4 and 8 to get 12.
5\left(-4\right)^{3}
Cancel out \left(-4\right)^{12}\times 5^{4} in both numerator and denominator.
5\left(-64\right)
Calculate -4 to the power of 3 and get -64.
-320
Multiply 5 and -64 to get -320.