25^15>(-8)^10 x 3^30

k cho mình nhé

\(25^{15}=5^{30}\)

\(8^{10}\cdot3^{30}=6^{30}\)

Do đó: \(25^{15}< 8^{10}\cdot3^{30}\)

Ta có:

8¹⁰ . 3³⁰ = ( 2³)¹⁰ . 3³⁰

= 2³⁰ . 3³⁰

= 6³⁰

= (6²)¹⁵

⁼ 36¹⁵

Vì 25<36

=>25¹⁵ < 36¹⁵

hay 25¹⁵ < 8¹⁰ . 3³⁰

t cung k biet giai bai nay 

25^15=(5^2)^15=5^30

8^10.3^30=(2^3)^10.3^30=2^30.3^30=6^30

mà 5^30 <6^30 nên 25^15 <8^10.3^30

25^15=(5^2)^15=5^30

8^10.3^30=(2^3)^10.3^30=2^30.3^30=6^30

Vì 5<6

nên 25^15<8^10.3^30

K mình nha

a) Ta có: \(25^{15}=\left(5^2\right)^{15}=5^{30}\)

               \(8^{10}.3^{30}=\left(2^3\right)^{10}.3^{30}\)\(=2^{30}.3^{30}=6^{30}\)

Vì \(5^{30}< 6^{30}\)nên \(25^{15}< 8^{10}.3^{30}\)

b) Ta có: \(\frac{4^{15}}{7^{30}}=\frac{\left(2^2\right)^{15}}{7^{30}}=\frac{2^{30}}{7^{30}}\)

\(\frac{8^{10}.3^{30}}{7^{30}.4^{15}}=\frac{\left(2^3\right)^{10}.3^{30}}{7^{30}.\left(2^2\right)^{15}}=\frac{2^{30}.3^{30}}{7^{30}.2^{30}}=\frac{3^{30}}{7^{30}}\)

Vì \(2^{30}< 3^{30}\)nên \(\frac{2^{30}}{7^{30}}< \frac{3^{30}}{7^{30}}\)hay \(\frac{4^{15}}{7^{30}}< \frac{8^{10}.3^{30}}{7^{30}.4^{15}}\)

_Học tốt_

                                                                Bài giải

\(25^{15}=\left(5^2\right)^{15}=5^{30}\)

\(8^{10}\cdot3^{30}=\left(2^3\right)^{10}\cdot3^{30}=2^{30}\cdot3^{30}=\left(2\cdot3\right)^{30}=6^{30}\)

Vì \(5^{30}< 6^{30}\) nên \(25^{15}< 8^{10}\cdot3^{30}\)