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SMK Teknologi dan Rekayasa

Indikator UN 2011 Matematika SMK Teknologi (3)


Indikator 3
Menentukan hasil operasi bilangan berpangkat

Bentuk sederhana dari \frac{\sqrt[6]{64x^{8}y^{12}}}{\sqrt[3]{x}} adalah ….
a. 2x^{3}y
b. 2x^{3}y^{2}
c. 2xy^{2}
d. 2x^{2}y^{3}
e. 4x^{3}y^{2}
Jawaban: c
\begin{array}{rcl}\frac{\sqrt[6]{64x^{8}y^{12}}}{\sqrt[3]{x}}&=&\frac{\big(64x^{8}y^{12}\big)^{\frac{1}{6}}}{\big(x\big)^{\frac{1}{3}}}\\\\&=&\frac{\big(2^{6}x^{8}y^{12}\big)^{\frac{1}{6}}}{x^{\frac{1}{3}}}\\\\&=&\frac{\big(2^{6}\big)^{\frac{1}{6}}\big(x^{8}\big)^{\frac{1}{6}}\big(y^{12}\big)^{\frac{1}{6}}}{x^{\frac{1}{3}}}\\\\&=&\frac{2^{6\times \frac{1}{6}}x^{8\times \frac{1}{6}}y^{12\times \frac{1}{6}}}{x^{\frac{1}{3}}}\\\\&=&\frac{2x^{\frac{4}{3}}y^{2}}{x^{\frac{1}{3}}}\\\\&=&2x^{\frac{4}{3}}x^{-\frac{1}{3}}y^{2}\\\\&=&2x^{\frac{4}{3}+\big(-\frac{1}{3}\big)}y^{2}\\\\&=&2xy^{2}\end{array}

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