Question

viết các biểu thức sau dưới dạng lũy thừa của 1 số hữu tỉ

a. \(8^{15}.4^{13}\)

b. \(\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{4}\right)^{28}\)

c. \(9^{12}.27^{10}\)

 

Answer 1

a) \(8^{15}.4^{13}=\left(2^3\right)^{15}.\left(2^2\right)^{13}=2^{45}.2^{26}=2^{71}\)

b) \(\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{4}\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2^2}\right)^{28}=\frac{1}{2^{18}}.\frac{1}{2^{56}}=\frac{1}{2^{74}}=\left(\frac{1}{2}\right)^{74}\)

c) \(9^{12}.27^{10}=\left(3^2\right)^{12}.\left(3^3\right)^{10}=3^{24}.3^{30}=3^{54}\)

Answer 2

a) = (2³)¹⁵. (2²)¹³ = 2⁴⁵.2²⁶ = 2⁷¹

b) = \(\left(\frac{1}{2}\right)^{18}.\left(\left(\frac{1}{2}\right)^2\right)^{28}=\left(\frac{1}{2}\right)^{18}.\left(\frac{1}{2}\right)^{56}=\left(\frac{1}{2}\right)^{18+56}=\left(\frac{1}{2}\right)^{74}\)

c) = (3²)¹².(3³)¹⁰ = 3²⁴.3³⁰ = 3²⁴⁺³⁰ = 3⁵⁴