Simplify the expression (3x^4/2y^3)^2

1 answer:

8 0

Simplify the following:
((3 x^4 y^3)/2)^2
Multiply each exponent in (3 x^4 y^3)/2 by 2:
(3^2 x^(2×4) y^(2×3))/(2^2)
2×4 = 8:
(3^2 x^8 y^(2×3))/2^2
2×3 = 6:
(3^2 x^8 y^6)/2^2
2^2 = 4:
(3^2 x^8 y^6)/4
3^2 = 9:
Answer: (9 x^8 y^6)/4

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$\text{If}\ a_1,\ a_2,\ a_3,\ a_4,\ ...,\ a_n\ \text{is the geometric sequence, then}\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=...=\dfrac{a_n}{a_{n-1}}=constant=r-\text{common ration}.\\\\\text{We have}\ \dfrac{1}{2},\ \dfrac{1}{3},\ \dfrac{2}{9},\ \dfrac{4}{27},\ ...\\\\\dfrac{\frac{1}{3}}{\frac{1}{2}}=\dfrac{1}{3}\cdot\dfrac{2}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{2}{9}}{\frac{1}{3}}=\dfrac{2}{9}\cdot\dfrac{3}{1}=\dfrac{2}{3}\\\\\dfrac{\frac{4}{27}}{\frac{2}{9}}=\dfrac{4}{27}\cdot\dfrac{9}{2}=\dfrac{2}{3}$

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