Bab Eksponen dan Logaritma - Sifat-sifat Eksponen

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Mathematics

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10th Grade

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Practice Problem

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Supaat Supaat

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13 Slides • 4 Questions

Sifat-sifat Bilangan Berpangkat

Supaat, M.Pd

Sifat 1

Perkalian Bilangan Berpangkat

Misalkan $a$ adalah bilangan real. Sedangkan, $m$ dan $n$ masing-masing adalah bilangan asli.

Selanjutnya, berlaku

$a^m\times a^n=a^{m+n}$

Contoh 1.1

$2^3\times2^2=...$

Contoh 1.2

Nyatakan sebagai bilangan berpangkat paling sederhana
$9\times27=...$

Sifat 2

Pembagian Bilangan Berpangkat

Misalkan $a$ adalah bilangan real tak-nol. Sedangkan, $m$ dan $n$ masing-masing adalah bilangan asli.

Selanjutnya, berlaku

\frac{a^m}{a^n}=a^{m-n}

untuk

m>n

\frac{a^m}{a^n}=\frac{1}{a^{n-m}}

untuk

m<n

Contoh 2.1

$\frac{5^5}{5^3}=...$

Contoh 2.2

$\frac{2^3}{2^7}=...$

Sifat 3

Pangkat dari Perkalian dan Pembagian

Misalkan $a$ dan $b$ masing-masing bilangan real. Sedangkan, $n$ adalah bilangan asli.

Selanjutnya, berlaku

$\left(a\times b\right)^n=a^n\times b^n$

$\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$ asalkan $b\ne0$

Contoh 3.1

$\left(2\times7\right)^3=...$

Contoh 3.2

$\left(\frac{2}{7}\right)^3=...$

Sifat 4

Pangkat dari Bilangan Berpangkat

Misalkan $a$ adalah bilangan real. Sedangkan, $m$ dan $n$ masing-masing merupakan bilangan asli.

Selanjutnya, berlaku

$\left(a^m\right)^n=a^{m\times n}$

Contoh 4.1

$\left(2^3\right)^2=...$

Contoh 4.2

Nyatakan dalam bentuk bilangan-bilangan prima berpangkat paling sederhana

\left(\frac{8}{9}\right)^5=...

Multiple Choice

Nyatakan dalam bentuk bilangan-bilangan prima brpangkat yang paling sederhana

\left(\frac{35}{27}\right)^3=...

$\frac{5^3\times7^3}{3^9}$

$\frac{5^3\times7^3}{3^6}$

$\frac{5^3+7^3}{3^9}$

$\frac{5^3+7^3}{3^6}$

Multiple Choice

Nyatakan dalam bentuk bilangan-bilangan prima brpangkat yang paling sederhana

\left(1000\right)^3\times\left(\frac{8}{5}\right)^4=...

$2^{21}\times5^5$

$\frac{2^{15}}{5}$

$2^{13}\times5^2$

$2^{18}\times5^5$

Multiple Choice

Misalkan $a$ dan $b$ adalah bilangan-bilangan real tak-nol. Bentuk paling sederhana dari

$\left(\frac{a^3}{b^2}\right)^5\div\left(a^2\cdot b\right)^3=...$

$\frac{a^9}{b^{13}}$

$\frac{a^9}{b^7}$

$\frac{a^{21}}{b^{13}}$

$\frac{a^{21}}{b^7}$

Multiple Choice

Misalkan $a$ dan $b$ adalah bilangan-bilangan real tak-nol. Bentuk paling sederhana dari

$\left(\frac{8a^2b}{9a^4b^3}\right)^5\div\left(\frac{27a^3}{4b^2}\right)^4=...$

$\frac{2^{23}}{3^{22}a^{22}b^2}$

$\frac{2^73^2a^2}{b^{13}}$

$\frac{2^{23}a^2}{3^2b^{10}}$

$\frac{2^7a^2}{3^{22}b^2}$

Sifat-sifat Bilangan Berpangkat

Supaat, M.Pd

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