Berikut ini Contoh Soal dan Pembahasan dari Materi Matematika Eksponen, dan semoga bermanfaat bagi kita semua
SOAL No. 1
Diketahui $a=\frac{1}{2},$ b = 2, dan c = 1. Nilai dari $\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ adalah....
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}} = \left ( a \right )^{-2-1}.\left ( b \right )^{1-2}.\left ( c \right )^{3-\left ( -1 \right )}$
Pembahasan
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\left ( a \right ) ^{-3}.\left (b \right )^{-1}.\left ( c \right )^{4}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\left ( 2 ^{-1}\right )^{-3}.\left ( 2 \right )^{-1}.\left ( 1 \right )^{4}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\left ( 2 \right )^{3}.\left ( 2 \right )^{-1}.\left ( 1 \right )^{4}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\frac{2^{3}}{2}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=4$
SOAL No. 2
Bentuk sederhana dari $\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$ adalah......?
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\left ( 2 ^{-1}\right )^{-3}.\left ( 2 \right )^{-1}.\left ( 1 \right )^{4}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\left ( 2 \right )^{3}.\left ( 2 \right )^{-1}.\left ( 1 \right )^{4}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=\frac{2^{3}}{2}$
$\frac{a^{-2}.b.c^{3}}{ab^{2}c^{3}}$ $=4$
SOAL No. 2
Bentuk sederhana dari $\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$ adalah......?
Pembahasan
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}=\left ( \frac{7}{84} \right )\left ( \frac{x^{3}}{x^{-7}} \right )\left ( \frac{y^{-4}}{y^{-1}} \right )\left ( \frac{z^{-6}}{z^{-4}} \right )$
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$$=\left ( \frac{1}{12} \right )\left (x ^{3-\left ( -7 \right )} \right )\left ( \frac{1}{y^{-1-\left ( -4 \right )}} \right )\left ( \frac{1}{z^{-4-\left ( -6 \right )}} \right )$
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$$=\left ( \frac{1}{12} \right )\left (x ^{10} \right )\left ( \frac{1}{y^{3}} \right )\left ( \frac{1}{z^{2}} \right )$
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$$=\frac{x^{10}}{12y^{3}z^{2}}$
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$$=\left ( \frac{1}{12} \right )\left (x ^{10} \right )\left ( \frac{1}{y^{3}} \right )\left ( \frac{1}{z^{2}} \right )$
$\frac{7x^{3}y^{-7}z^{-6}}{84x^{-7}y^{-1}z^{-4}}$$=\frac{x^{10}}{12y^{3}z^{2}}$
Lanjut ke Soal No 3 dan 4
