Answer:
[tex]A. (5n^{-3})^4\\E. (25n^{-6})^{2}[/tex]
Step-by-step explanation:
We are asked to determine which expressions out of the options simplifies to:
[tex]\dfrac{625}{n^{12}}=625n^{-12}[/tex]
[tex]A. (5n^{-3})^4=5^4*n^{-3*4}=625n^{-12}\\B. (5n^{-3})^{-4}=5^{-4}*n^{-3*-4}=\frac{1}{625}n^{12}\\C. (5n^{-4})^3=5^3*n^{-4*3}=125n^{-12}\\\\D. (25n^{-6})^{-2}=25^{-2}*n^{-6*-2}=\frac{1}{625}n^{12}\\\\E. (25n^{-6})^{2}=25^{2}*n^{-6*2}=625n^{-12}\\\\F. (25n^{2})^{-6}=25^{-6}*n^{2*-6}=\frac{1}{25^6}n^{-12}[/tex]
From the above results, we can see that only options A and E are equivalent to the given expression.
