Jika a=2 dan b=3, tentukan nilai dari a. (a^(-1) + b^(-1))/(a^(-2) + b^(-2)) b. (a-b)^(-3) · ((a+b)/(b-a))^(-2) · 1/(a+b)^(-3) c. 1/(1-1/(a+b^(-1)))

<p>Jawaban :&nbsp;</p><p>a. (a^(-1) + b^(-1))/(a^(-2) + b^(-2)) = 30/13</p><p>b. (a-b)^(-3) · ((a+b)/(b-a))^(-2) · 1/(a+b)^(-3) = -5</p><p>c. 1/(1-1/(a+b^(-1))) = 7/4</p><p>&nbsp;</p><p>Ingat!<br>(a^(m))^(n) = a^(mn)</p><p>a^(m) x a^(n) = a^(m+n)</p><p>a^(m) : a^(n) = a^(m-n)</p><p>(a/b)^m = a^m/b^m</p><p>a^(0) = 1, jika a ≠0</p><p>a^(-n) = 1/a^(n)</p><p>&nbsp;</p><p>Diketahui a=2 dan b=3</p><p>&nbsp;</p><p>Sehingga&nbsp;</p><p>a. (a^(-1) + b^(-1))/(a^(-2) + b^(-2))&nbsp;</p><p>= (2^(-1) + 3^(-1))/(2^(-2) + 3^(-2))&nbsp;</p><p>= (1/2^(1) + 1/3^(1))/(1/2^(2) + 1/3^(2))&nbsp;</p><p>= (1/2 + 1/3)/(1/4 + 1/9)&nbsp;</p><p>= (5/6)/(13/36)&nbsp;</p><p>= (30/36)/(13/36)&nbsp;</p><p>= 30/13</p><p>&nbsp;</p><p>b. (a-b)^(-3) · ((a+b)/(b-a))^(-2) · 1/(a+b)^(-3)&nbsp;</p><p>= (a-b)^(-3) · ((a+b)/(b-a))^(-2) · 1/(a+b)^(-3)&nbsp;</p><p>= (2-3)^(-3) · ((2+3)/(3-2))^(-2) · 1/(2+3)^(-3)&nbsp;</p><p>= (-1)^(-3) · ((5)/(1))^(-2) · 1/(5)^(-3)&nbsp;</p><p>= 1/(-1)^(3) · 5^(-2) · 5^(3)&nbsp;</p><p>= 1/(-1) · 5^(-2+3)&nbsp;</p><p>= -1 · 5^(1)&nbsp;</p><p>= -1 · 5</p><p>= -5</p><p>&nbsp;</p><p>c. 1/(1-1/(a+b^(-1)))</p><p>= 1/(1-1/(2+3^(-1)))</p><p>= 1/(1-1/(2+1/3))</p><p>= 1/(1-1/(7/3))</p><p>= 1/(1-3/7)</p><p>= 1/(4/7)</p><p>= 7/4</p><p>&nbsp;</p><p>Jadi, jawabannya adalah&nbsp;</p><p>a. (a^(-1) + b^(-1))/(a^(-2) + b^(-2)) = 30/13</p><p>b. (a-b)^(-3) · ((a+b)/(b-a))^(-2) · 1/(a+b)^(-3) = -5</p><p>c. 1/(1-1/(a+b^(-1))) = 7/4</p>