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harina [27]
3 years ago
6

Simplify (5x^7y^3z^-1)^2x(2xy^-5)^3x(2y^-3z^2)^3

Mathematics
1 answer:
juin [17]3 years ago
8 0
Remember
(abc)^x=(a^x)(b^x)(c^x)
and
(x^m)(x^n)=x^{m+n}
and
(x^m)^n=x^{mn}
and
x^{-m}= \frac{1}{x^m}
so

(5x^7y^3z^{-1})^2(2xy^{-5})^3(2y^{-3}z^2)^3=
(5^2)((x^7)^2)((y^3)^2)((z^{-1})^2)(2^3)(x^3)((y^{-5})^3)(2^3)((y^{-3})^3)((z^2)^3)=
(25)(x^{14})(y^6)(z^{-2})(8)(x^3)(y^{-15})(8)(y^{-9})(z^6)=
1600x^{17}y^{-18}z^4=
\frac{1600x^{17}z^4}{y^{18}}
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