kasih penjelasan dong biar paham

Berikut ini adalah pertanyaan dari jdcok21 pada mata pelajaran Matematika untuk jenjang Sekolah Dasar

Kasih penjelasan dong biar paham

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

Nomor 1.

Sifat-sifat operasi bilangan berpangkat :

$\boxed{\boxed{\begin{array}{ll}a^b\times a^c=a^{(b+c)}&\frac{a^b}{a^c}=a^{(b-c)}\\~\\\left(a^b\right)^c=a^{(b\times c)}\end{array}}}$

$\frac{16^\frac{1}{2}.9^2.4^\frac{2}{3}}{16^\frac{1}{4}.9^\frac{1}{2}.4^\frac{1}{6}}$

$=\frac{\left(2^4\right)^\frac{1}{2}.\left(3^2\right)^2.\left(2^2\right)^\frac{2}{3}}{\left(2^4\right)^\frac{1}{4}.\left(3^2\right)^\frac{1}{2}.\left(2^2\right)^\frac{1}{6}}$

$=\frac{2^{\left(4\times \frac{1}{2}\right)}.3^{(2\times 2)}.2^{\left(2\times \frac{2}{3}\right)}}{2^{\left(4\times \frac{1}{4}\right)}.3^{\left(2\times \frac{1}{2}\right)}.2^{\left(2\times \frac{1}{6}\right)}}$

$=\frac{2^2.3^4.2^\frac{4}{3}}{2^1.3^1.2^\frac{1}{3}}$

$=\frac{2^{\left(2+\frac{4}{3}\right)}.3^4}{2^{\left(1+\frac{1}{3}\right)}.3^\frac{2}{3}}$

$=\frac{2^\frac{10}{3}.3^4}{2^\frac{4}{3}.3^1}$

$=2^{\left(\frac{10}{3}-\frac{4}{3}\right)}.3^{(4-1)}$

$=2^2.3^3$

$=4\times 27$

$=108$

$\therefore \boxed{\boxed{\frac{16^\frac{1}{2}.9^2.4^\frac{2}{3}}{16^\frac{1}{4}.9^\frac{1}{2}.4^\frac{1}{6}}=2^2.3^3=108}}$

$\\$

Nomor 2.

Sifat-sifat operasi bilangan logaritma :

$\boxed{\boxed{\begin{array}{l}^a\log~b+~^a\log~c=~^a\log~(b\times c)\\~\\^a\log~b-~^a\log~c=~^a\log~\frac{b}{c}\\~\\^a\log~a^b=b.^a\log~a\\~\\^a\log~a=1\end{array}}}$