Question

Which is the value of this expression when a = 5 and k = negative 2? (3^2 a^-3)(3 a^-4)^-2

Answer 1

Answer:

$5^5=3125$

Step-by-step explanation:

$Given\ (3^2a^{-3})(3a^{-4})^{-2}\\\\=3^2a^{-3}\cdot(3)^{-2}(a^{-4})^{-2}\\\\=3^2\times3^{-2}\times a^{-3}\times a^8\ \ \ \ \ \ (x^{-m})^{-n}=x^{mn}\\\\=3^{2-2}\times a^{-3+8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^m\times x^n=x^{m+n}\\\\=3^0\times a^5\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x^0=1\\\\=1\times a^5\\\\=a^5\\\\put\ value\ a=5\\\\=5^5\\\\=3125$