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Sifat-Sifat Eksponen:
[tex]\begin{gathered} \begin{array}{ | c | c| c | } \hline\ \ \text{No}& \text{bentuk}& \text{penyederhanaan} \\ \hline 1 & a {}^{m} \times a {}^{n} &a {}^{(m + n)} \\ \hline 2 & (a {}^{m} ) {}^{n} &a {}^{(m \times n)} \\ \hline 3 & a {}^{n} \times {b}^{n} &(ab) {}^{n} \\ \hline 4 & a {}^{n} \div {b}^{n} &( \frac{a}{b} ) {}^{n} \\ \hline 5 & \frac{a {}^{m} }{ {a}^{n} } &a {}^{(m - n)} \\ \hline 6 & a {}^{0} &1 \: (a≠0) \\ \hline 7 & a {}^{ - n} & \frac{1}{a {}^{n} } \\ \hline 8 & a {}^{ \frac{m}{n} } & \sqrt[n]{a {}^{m} } \\ \hline 9 & ( \frac{a}{b}) {}^{ - n} & (\frac{b}{a} ) {}^{n} \\ \hline 10 & ( \frac{a}{b} ) {}^{n} & \frac{a {}^{n} }{ {b}^{n} } \\ \hline \end{array}\end{gathered}[/tex]
[tex]\begin{aligned} (64)^{-\frac{1}{3}} &= \frac{1}{64^{ \frac{1}{3}} }\\&= \frac{1}{(2^6)^{ \frac{1}{3}}} \\&= \frac{1}{2^{ \frac{6}{3}}} \\&= \frac{1}{2^2} \\&= \boxed{\bold{\frac{1}{4}}} \end{aligned}[/tex]
[tex]\begin{array}{lr}\texttt{Selamat Hari Pemadam Kebakaran Internasional}\end{array}[/tex]
[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 04 - 05 - 2023}}[/tex]
Penjelasan dengan langkah-langkah:
[tex] = {(64)}^{ - \frac{1}{3} } [/tex]
[tex] = {( {4}^{ \cancel3}) }^{ - \frac{1}{ \cancel3} } [/tex]
[tex] = {(4)}^{ - 1} [/tex]
[tex] = \bold{\frac{1}{4}} [/tex]
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Eksponen
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Sifat-Sifat Eksponen:
[tex]\begin{gathered} \begin{array}{ | c | c| c | } \hline\ \ \text{No}& \text{bentuk}& \text{penyederhanaan} \\ \hline 1 & a {}^{m} \times a {}^{n} &a {}^{(m + n)} \\ \hline 2 & (a {}^{m} ) {}^{n} &a {}^{(m \times n)} \\ \hline 3 & a {}^{n} \times {b}^{n} &(ab) {}^{n} \\ \hline 4 & a {}^{n} \div {b}^{n} &( \frac{a}{b} ) {}^{n} \\ \hline 5 & \frac{a {}^{m} }{ {a}^{n} } &a {}^{(m - n)} \\ \hline 6 & a {}^{0} &1 \: (a≠0) \\ \hline 7 & a {}^{ - n} & \frac{1}{a {}^{n} } \\ \hline 8 & a {}^{ \frac{m}{n} } & \sqrt[n]{a {}^{m} } \\ \hline 9 & ( \frac{a}{b}) {}^{ - n} & (\frac{b}{a} ) {}^{n} \\ \hline 10 & ( \frac{a}{b} ) {}^{n} & \frac{a {}^{n} }{ {b}^{n} } \\ \hline \end{array}\end{gathered}[/tex]
Penyelesaian Soal
[tex]\begin{aligned} (64)^{-\frac{1}{3}} &= \frac{1}{64^{ \frac{1}{3}} }\\&= \frac{1}{(2^6)^{ \frac{1}{3}}} \\&= \frac{1}{2^{ \frac{6}{3}}} \\&= \frac{1}{2^2} \\&= \boxed{\bold{\frac{1}{4}}} \end{aligned}[/tex]
[tex]\begin{array}{lr}\texttt{Selamat Hari Pemadam Kebakaran Internasional}\end{array}[/tex]
[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 04 - 05 - 2023}}[/tex]
Penjelasan dengan langkah-langkah:
[tex] = {(64)}^{ - \frac{1}{3} } [/tex]
[tex] = {( {4}^{ \cancel3}) }^{ - \frac{1}{ \cancel3} } [/tex]
[tex] = {(4)}^{ - 1} [/tex]
[tex] = \bold{\frac{1}{4}} [/tex]