125 = 53; -125=(-5)3;27=33; -27= (-3)3

Ta có: (-8).(-3)3.(+125)

= (-2)3 . (-3)3 . 53

= [(-2).(-3)]3.53 = 63 . 53

= (6.5)3 = 303

a) 5³⁶ = 5¹² (5³)¹² = 125¹²; 11²⁴ = 11^2.12 = (11²)¹² = 121¹²

a: \(4^5\cdot8^7=2^{10}\cdot2^{21}=2^{31}\)

b: \(125^5\cdot25^3=5^{15}\cdot5^6=5^{21}\)

a) \(4^5\)x \(8^7\)

= \(\left(2^2\right)^5\) x \(\left(2^3\right)^7\)

= \(2^{10}\) x \(2^{21}\)

= \(2^{31}\)

b) \(125^5\) x \(25^3\)

= \(\left(5^3\right)^5\) x \(\left(5^2\right)^3\)

= \(5^{15}\) x \(5^6\)

= \(5^{21}\)

8² x 32⁴ = (2³)² x (2⁵)⁴ = 2⁶  x 2²⁰=2²⁶

27³ x 9⁴ x243 = 3⁹ x 3⁸x3⁵=3²²

64³ : 16³ =2¹⁸ : 2¹² = 2⁶

5¹³:125⁴ = 5¹³ : 5¹²= 5

\(\dfrac{9}{25}=\left(\dfrac{3}{5}\right)^2\)

\(\dfrac{8}{27}=\left(\dfrac{2}{3}\right)^3\)

\(\dfrac{-125}{64}=\left(-\dfrac{5}{4}\right)^3\)

\(0=0^2\)

\(-27=\left(-3\right)^3\)

\(\dfrac{16}{81}=\left(\dfrac{2}{3}\right)^4\)

\(125\times3\times9\times15=5^3\times3\times3^2\times3\times5=5^4\times3^4=\left(5\times3\right)^4=15^4\)

125.3.9.15=5⁴.3⁴

15⁴

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