Pembahasan Soal Ujian Nasional Matematika SMP Part 3

Soal 5 (Perpangkatan)

Hasil dari : ${\left( {{3^4}} \right)^2} \times {\left( {\frac{1}{3}} \right)^{ - 2}}$ adalah ....

A. 3¹²

B. 3¹⁰

C. 3⁸

D. 3⁶

Jawab:

$\begin{array}{l}  {\left( {{3^4}} \right)^2} \times {\left( {\frac{1}{3}} \right)^{ - 2}} \\   = \left( {{3^{4 \times 2}}} \right) \times {\left( {{3^{ - 1}}} \right)^{ - 2}} \\   = {3^8} \times {3^2} \\   = {3^{10}} \\  \end{array}$

Jawaban yang tepat adalah B.

Soal 6 (Bentuk Akar)

Bentuk:$\frac{2}{{3 - \sqrt 5 }}$ setara dengan ....

$\begin{array}{*{20}{c}}    {A.} & {\left( {3 + \sqrt 5 } \right)}  \\ \end{array}$

$\begin{array}{*{20}{c}}    {B.} & {\left( {3 - \sqrt 5 } \right)}  \\ \end{array}$

$\begin{array}{*{20}{c}}    {C.} & {\frac{{\left( {3 + \sqrt 5 } \right)}}{2}}  \\ \end{array}$

$\begin{array}{*{20}{c}}    {D.} & {\frac{{\left( {3 - \sqrt 5 } \right)}}{2}}  \\ \end{array}$

Jawab:

$\begin{array}{l}  \frac{2}{{3 - \sqrt 5 }} \\   = \frac{2}{{3 - \sqrt 5 }} \times \frac{{3 + \sqrt 5 }}{{3 + \sqrt 5 }} \\   = \frac{{2\left( {3 + \sqrt 5 } \right)}}{{\left( {3 - \sqrt 5 } \right)\left( {3 + \sqrt 5 } \right)}} \\   = \frac{{2\left( {3 + \sqrt 5 } \right)}}{{\left( {{3^2} - {{\left( {\sqrt 5 } \right)}^2}} \right)}} \\   = \frac{{2\left( {3 + \sqrt 5 } \right)}}{{\left( {9 - 5} \right)}} \\   = \frac{{2\left( {3 + \sqrt 5 } \right)}}{4} \\   = \frac{{3 + \sqrt 5 }}{2} \\  \end{array}$

Jawaban yang tepat adalah C.