Question

Przedstaw wyrażenie w prostszej postaci. Pilne na jutro.
WYNIKI
a) a⁸
b) x⁴y⁴
c) 8xy ​

Answer 1

Verified answer

a)

[tex]\left[\left(a^2\cdot a^3\right)^2:\left(a^3:a\right)^2\right]\cdot\left[\left(a^2\right)^3:a^4\right]=\left[\left(a^5\right)^2:\left(a^2\right)^2\right]\cdot\left[a^6:a^4\right]=[/tex]

[tex]=\left[a^{10}:a^4\right]\cdot\left[a^2\right]=a^6\cdot a^2=a^8[/tex]

b)

[tex]\dfrac{\left(x^2\cdot y^3\right)^4:\left(x\cdot y^2\right)^3}{\left(x^3\cdot y^2\right)^3:\left(x^4\cdot y^2\right)^2}=\dfrac{\left(x^8y^{12}\right):\left(x^3y^6\right)}{\left(x^9y^6\right):\left(x^8y^4\right)}=\dfrac{x^5y^6}{xy^2}=x^4y^4[/tex]

c)

[tex]\dfrac{2xy^2\cdot\left[\left(4x^2\cdot y^3\right)^3:\left(2x\cdot y^4\right)^2\right]}{\left(-2x^2 y\right)^2}=\dfrac{2xy^2\cdot\left(64x^6y^9\right):\left(4x^2y^8\right)}{4x^4 y^2}=[/tex]

[tex]=\dfrac{2xy^2\cdot16x^4y}{4x^4 y^2}=\dfrac{32x^5y^3}{4x^4 y^2}=8xy[/tex]