Question

Viết biểu thức sau dưới dạng 1 lũy thừa:
a) 12⁸.9¹²
b) 45¹⁰.5³⁰

Answer 1

a) 3^8.4^8.3^24=3^32.2^16

b) 5^10.3^20.5^30=5^40.3^20

Answer 2

\(a)12^8\cdot9^{12}\)

\(=\left(2^2\cdot3\right)^8\cdot\left(3^2\right)^{12}\)

\(=\left(2^2\right)^8\cdot3^8\cdot3^{24}\)

\(=2^{16}\cdot3^{32}\)

\(=2^{16}\cdot\left(3^2\right)^{16}\)

\(=2^{16}\cdot9^{16}\)

\(=\left(2\cdot9\right)^{16}\)

\(=18^{16}\)

Answer 3

b) =25^20.3^20=(25.3)^20=75^20

Answer 4

\(b)45^{10}\cdot5^{30}\)

\(=45^{10}\cdot\left(5^3\right)^{10}\)

\(=45^{10}\cdot125^{10}\)

\(=\left(45\cdot125\right)^{10}\)

\(=5625^{10}\)