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((x^(2)y^(2)z^(2))^(5))/((x^(3)y^(3)z^(3))^(7)) Which of the following is equivalent to the given expression? Choose 1 answer: (A) (x^(-2)y^(-2)z^(-2))^(5)(x^(3)y^(3)z^(3))^(7) (B) (x^(5)y^(5)z^(5))^(2)(x^(-3)y^(-3)z^(-3))^(7) (c) ((x^(5)y^(5)z^(5))^(8))/((x^(7)y^(7)z^(7))^(27)) (D) ((x^(5)y^(5)z^(5))^(6))/((x^(7)y^(7)z^(7))^(9))

(x2y2z2)5(x3y3z3)7 \frac{\left(x^{2} y^{2} z^{2}\right)^{5}}{\left(x^{3} y^{3} z^{3}\right)^{7}} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) (x−2y−2z−2)5(x3y3z3)7 \left(x^{-2} y^{-2} z^{-2}\right)^{5}\left(x^{3} y^{3} z^{3}\right)^{7} \newline(B) (x5y5z5)2(x−3y−3z−3)7 \left(x^{5} y^{5} z^{5}\right)^{2}\left(x^{-3} y^{-3} z^{-3}\right)^{7} \newline(C) (x5y5z5)8(x7y7z7)27 \frac{\left(x^{5} y^{5} z^{5}\right)^{8}}{\left(x^{7} y^{7} z^{7}\right)^{27}} \newline(D) (x5y5z5)6(x7y7z7)9 \frac{\left(x^{5} y^{5} z^{5}\right)^{6}}{\left(x^{7} y^{7} z^{7}\right)^{9}}

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Full solution

Q. (x2y2z2)5(x3y3z3)7 \frac{\left(x^{2} y^{2} z^{2}\right)^{5}}{\left(x^{3} y^{3} z^{3}\right)^{7}} \newlineWhich of the following is equivalent to the given expression?\newlineChoose 11 answer:\newline(A) (x−2y−2z−2)5(x3y3z3)7 \left(x^{-2} y^{-2} z^{-2}\right)^{5}\left(x^{3} y^{3} z^{3}\right)^{7} \newline(B) (x5y5z5)2(x−3y−3z−3)7 \left(x^{5} y^{5} z^{5}\right)^{2}\left(x^{-3} y^{-3} z^{-3}\right)^{7} \newline(C) (x5y5z5)8(x7y7z7)27 \frac{\left(x^{5} y^{5} z^{5}\right)^{8}}{\left(x^{7} y^{7} z^{7}\right)^{27}} \newline(D) (x5y5z5)6(x7y7z7)9 \frac{\left(x^{5} y^{5} z^{5}\right)^{6}}{\left(x^{7} y^{7} z^{7}\right)^{9}}
  1. Simplify Expression: Simplify the given expression using the properties of exponents.\newlineThe original expression is (x2y2z2)5(x3y3z3)7\frac{(x^{2}y^{2}z^{2})^{5}}{(x^{3}y^{3}z^{3})^{7}}.\newlineUsing the power of a product property, (a∗b)n=an∗bn(a*b)^{n} = a^{n} * b^{n}, we can rewrite the expression as:\newlinex2∗5y2∗5z2∗5x3∗7y3∗7z3∗7\frac{x^{2*5}y^{2*5}z^{2*5}}{x^{3*7}y^{3*7}z^{3*7}}.
  2. Apply Power Property: Now, simplify the exponents by multiplying them. x10y10z10x21y21z21\frac{x^{10}y^{10}z^{10}}{x^{21}y^{21}z^{21}}.
  3. Simplify Exponents: Next, apply the quotient of powers property, which states that anam=an−m\frac{a^n}{a^m} = a^{n-m}, to each variable separately.x10−21y10−21z10−21x^{10-21}y^{10-21}z^{10-21}.
  4. Apply Quotient Property: Subtract the exponents to simplify further. x(−11)y(−11)z(−11)x^{(-11)}y^{(-11)}z^{(-11)}.
  5. Subtract Exponents: The simplified expression is x−11y−11z−11x^{-11}y^{-11}z^{-11}, which can be rewritten using the negative exponent rule, a−n=1ana^{-n} = \frac{1}{a^n}, as:\newline1x11y11z11\frac{1}{x^{11}y^{11}z^{11}}.
  6. Rewrite with Negative Exponents: Now, let's compare the simplified expression with the answer choices.\newline(A) (x−2y−2z−2)5(x3y3z3)7(x^{-2}y^{-2}z^{-2})^{5}(x^{3}y^{3}z^{3})^{7} does not match our simplified expression.\newline(B) (x5y5z5)2(x−3y−3z−3)7(x^{5}y^{5}z^{5})^{2}(x^{-3}y^{-3}z^{-3})^{7} does not match our simplified expression.\newline(C) ((x5y5z5)8)/((x7y7z7)27)((x^{5}y^{5}z^{5})^{8})/((x^{7}y^{7}z^{7})^{27}) does not match our simplified expression.\newline(D) ((x5y5z5)6)/((x7y7z7)9)((x^{5}y^{5}z^{5})^{6})/((x^{7}y^{7}z^{7})^{9}) does not match our simplified expression.\newlineNone of the answer choices match the simplified expression 1/(x11y11z11)1/(x^{11}y^{11}z^{11}).

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