[(^(4)√x - 1/^(5)√x^(2))(^(4)√x + 1/^(5)√x^(2))]/^(20)^(4)√x - 1/^(5)√x^(2)x

<p>Jawaban : [x^(1/2) - x^(-4/5)]/[x^(1/4) - x^(3/5)]</p><p>&nbsp;</p><p>Ingat!<br>^(n)√(a^(m)) = a^(m/n)</p><p>a^(-n) = 1/a^(n)</p><p>a^(m) x a^(n) = a^(m+n)</p><p>(a^(m))^(n) = a^(mn)</p><p>&nbsp;</p><p>Asumsi soal:</p><p>[(^(4)√x - 1/^(5)√x^(2))(^(4)√x + 1/^(5)√x^(2))]/[^(4)√x - 1/^(5)√x^(2) x]</p><p>&nbsp;</p><p>Sehingga</p><p>&nbsp;[(^(4)√x - 1/^(5)√x^(2))(^(4)√x + 1/^(5)√x^(2))]/[^(4)√x - 1/^(5)√x^(2) x]</p><p>= [(x^(1/4) - 1/(x^(2/5)))(x^(1/4) + 1/(x^(2/5)))]/[x^(1/4) - 1/x^(2/5) x]</p><p>= [(x^(1/4))^(2) - (1/(x^(2/5)))^(2)]/[x^(1/4) - x^(-2/5) x]</p><p>= [x^(1/2) - 1/(x^(4/5))]/[x^(1/4) - x^(-2/5+1)]</p><p>= [x^(1/2) - x^(-4/5)]/[x^(1/4) - x^(3/5)]</p><p>= [x^(1/2) - x^(-4/5)]/[x^(1/4) - x^(3/5)]&nbsp;</p><p>&nbsp;</p><p>Jadi, [(^(4)√x - 1/^(5)√x^(2))(^(4)√x + 1/^(5)√x^(2))]/[^(4)√x - 1/^(5)√x^(2) x] = [x^(1/2) - x^(-4/5)]/[x^(1/4) - x^(3/5)]</p>