47.

a) ( - 3 )² . ( -3 )³ = ( -3 )⁵

b) ( -0,25 )³ : ( - 0,25 ) = ( -0,25 )² = ( 0,25 )²

c) [( -0,5 )² ]³ = ( -0,5 )^2.3 = ( -0,5 )⁶ = ( 0,5 )⁶

d) ( -0,01 )⁰ = 1

48. 

a) 7⁵ . 2⁵ = ( 7 . 2 )⁵ = 14⁵

b) 16⁴ . 2⁷ = ( 2⁴ )⁴ . 2⁷ = 2¹⁶ . 2⁷ = 2²³

c) 8² : 49³ = ( 2³ )² : ( 7² )³ = 2⁶ : 7⁶ = \(\left(\frac{2}{7}\right)^6\)

d) ( 0,3 )³ . 70³ = ( 0,3 . 70 )³ = 21³

49. 

( 0,04 )⁵ = \(\left(\frac{1}{25}\right)^5=\left[\left(\frac{1}{5}\right)^2\right]^5=\left(0,2\right)^{10}\)

( 0,008 )³ = \(\left(\frac{1}{125}\right)^3=\left[\left(\frac{1}{5}\right)^3\right]^3=\left(0,2\right)^9\)

( -0,0016 )² = \(\left(\frac{1}{625}\right)^2=\left[\left(\frac{1}{5}\right)^4\right]^2=\left(0,2\right)^8\)

50.

a) \(\frac{\left(-0,3\right)^7.2^8}{\left(0,6\right)^7}=\frac{\left(-0,3.2\right)^7.2}{\left(0,6\right)^7}=\frac{\left(-0,6\right)^7.2}{\left(0,6\right)^7}=-2\)

b) \(\frac{3^7.16^3}{12^5.27^2}=\frac{3^7.\left(2^4\right)^3}{\left(3.2^2\right)^5.\left(3^3\right)^2}=\frac{3^7.2^{12}}{3^5.\left(2^2\right)^5.3^6}=\frac{3^7.2^{12}}{2^{10}.3^{11}}=\frac{3^7.2^{10}.2^2}{3^7.2^{10}.3^4}=\frac{4}{81}\)

c) \(\frac{2^3.\left(0,5\right)^3.3^7}{2.\left(0,5\right)^4.3^8}=\frac{2^3.\left(0,5\right)^3.3^7}{2.\left(0,5\right)^4.3^8}=\frac{2.\left(0,5\right)^3.3^7.2^2}{2.\left(0,5\right)^3.3^7.0,5.3}=\frac{4}{1,5}=\frac{4}{\frac{3}{2}}=\frac{8}{3}\)

d) ( -1 )²⁰ + 1,69 . ( 3,5 - 2,2 )² - ( -1,69 )²

= 1 + 1,69 . ( 1,3 )² - 1,69 . 1,69

= 1 + 1,69 . [ ( 1,3 )² - 1,69 ]

= 1 + 1,69 . ( 1,69 - 1,69 )

= 1 + 0 = 1

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