Respuesta :

DTcath
The rules of exponents are:
multiplication=add the exponents
x^2.x^3=x^5
power=multiply the exponents
(x^2)^3=x^6

1. (4xy^2)^3(xy)^5
    (64x^3y^6)(x^5y^5)
    64x^8y^11
2. (2t^-3)^3(0.4r)^2
    (8t^-9)(0.16r^2)
    0.16r^2/8t^9 or r^2/50t^9
frika

Note main rules:

[tex]1.\quad (a\cdot b)^n=a^n\cdot b^n,\\ \\2.\quad a^m\cdot a^n=a^{m+n},\\ \\3.\quad (a^m)^n=a^{mn}.[/tex]

1. Consider expression [tex](4xy^2)^3(xy)^5.[/tex] Using previous rules:

  • 1 step: [tex](4xy^2)^3=4^3\cdot x^3\cdot (y^2)^3=64x^3y^{2\cdot 3}=64x^3y^6;[/tex]
  • 2 step: [tex](xy)^5=x^5\cdot y^5;[/tex]
  • 3 step: [tex](4xy^2)^3(xy)^5=64x^3y^6x^5y^5=64x^{3+5}y^{6+5}=64x^8y^{11}.[/tex]

2. Consider expression [tex](2t^{-3})^3(0.4r)^2.[/tex]  Using previous rules:

  • 1 step: [tex](2t^{-3})^3=2^3\cdot (t^{-3})^3=8t^{-3\cdot 3}=8t^{-9};[/tex]
  • 2 step: [tex](0.4r)^2=0.4^2\cdot r^2=0.16r^2;[/tex]
  • 3 step: [tex](2t^{-3})^3(0.4r)^2=8t^{-9}\cdot 0.16r^2=8\cdot 0.16t^{-9}r^2=1.28t^{-9}r^2.[/tex]

Answer:

  1. [tex]64x^8y^{11};[/tex]
  2. [tex]1.28t^{-9}r^2.[/tex]

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