Question

Please look at the question and solve! Thanks!

Answer 1

`x^(27)y^(24)z^(51)`

Explanation:

`\left(((x^3yz^4)^2(xy^2z^3)^4)/(xy^2z^3)\right)^3=x^(3(3\cdot 2+1\cdot 4-1))y^(3(1\cdot 2+2\cdot 4-2))z^(3(4\cdot 2+3\cdot 4-3))\\\\=x^(3(6+4-1))y^(3(2+8-2))z^(3(8+12-3))=x^(27)y^(24)z^(51)`

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You can recognize that the denominator factor is also one of the numerator factors, so can be cancelled right away. Proceeding to evaluate inside parentheses first, we get ...

`\left(((x^3yz^4)^2(xy^2z^3)^4)/(xy^2z^3)\right)^3=\left((x^3yz^4)^2(xy^2z^3)^3\right)^3\\\\=(x^6y^2z^8x^3y^6z^9)^3=(x^9y^8z^(17))^3\\\\=x^(27)y^(24)z^(51)`

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The rules of exponents that apply are ...

`(a^b)(a^c)=a^(b+c)\\\\(a^b)^c=a^(b\cdot c)`