Nilai (√(3^(2015)))/(√(3^2015) - √(3^(2013)) adalah ... a. (√3)/2 b. -(√3)/2 c. 3/2 d. 3/4

<p><strong>Jawaban: c. 3/2.</strong></p><p>&nbsp;</p><p><strong>Ingat!</strong></p><p><strong>Sifat Eksponen dan Bentuk Akar:</strong></p><ol><li><strong>√a = a^½</strong></li><li><strong>a^b × a^c = a^{b + c}</strong></li></ol><p>&nbsp;</p><p><strong>Sehingga untuk soal: [√(3²⁰¹⁵)]/{[√(3²⁰¹⁵)] − [√(3²⁰¹³)]}</strong></p><p>= (3^2015/2)/[(3^2015/2) − (3^2013/2)]</p><p>= (3^1007½)/[(3^1007½) − (3^1006½)]</p><p>= (3¹⁰⁰⁷√3)[(3¹⁰⁰⁷√3) − (3¹⁰⁰⁶√3)]</p><p>= [√3(3¹⁰⁰⁷)]/[√3(3¹⁰⁰⁷ − 3¹⁰⁰⁶)] <strong>(√3 dapat dicoret)</strong></p><p>= (3¹⁰⁰⁷)/(3¹⁰⁰⁷ − 3¹⁰⁰⁶)</p><p>= (3¹⁰⁰⁶ × 3)/[(3¹⁰⁰⁶ × 3) − 3¹⁰⁰⁶]</p><p>= (3¹⁰⁰⁶ × 3)/[3¹⁰⁰⁶(3 − 1)] <strong>(3¹⁰⁰⁶ dapat dicoret)</strong></p><p>= 3/(3 − 1)</p><p><strong>= 3/2.</strong></p><p>&nbsp;</p><p><strong><u>Dengan demikian, nilai dari [√(3</u>^<u>2015</u><u>)]/{[√(3</u>^<u>2015</u><u>)] − [√(3</u>^<u>2013</u><u>)]} adalah c. 3/2.</u></strong></p>