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tolongNo 7 - 10 pakai cara​

Berikut ini adalah pertanyaan dari uhm69 pada mata pelajaran Matematika untuk jenjang Sekolah Menengah Pertama

Tolong
No 7 - 10 pakai cara
​
tolongNo 7 - 10 pakai cara​

Jawaban dan Penjelasan

Berikut ini adalah pilihan jawaban terbaik dari pertanyaan diatas.

\mathbb \color{orange} \underbrace{PENYELESAIAN}

\boxed{ \: \displaystyle \begin{aligned} \tt a &= \tt \sqrt[n]{ {a}^{n} } \\ \tt {a}^{ \frac{m}{n} } &= \tt \sqrt[n]{ {a}^{m} } \\ \tt {a}^{ - n} &= \small \tt \frac{1}{ {a}^{n} } \end{aligned} \: } \\ \\

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SOAL 7a :

\displaystyle \begin{aligned} \tt \sqrt{18} &= \tt\sqrt{ \boxed {\tt9} \times 2} \\ &= \tt\sqrt{ \boxed{ \tt {3}}^{ \: \boxed{ \tt2}} \times 2} \\ &= \tt \boxed{ \tt3} \times \sqrt{2} \\ &= \tt \bf \boxed{ \bf3 }\sqrt{2} \end{aligned}

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SOAL 7b :

\displaystyle \begin{aligned} \tt \sqrt{80} &= \tt\sqrt{ \boxed {\tt16} \times 5} \\ &= \tt\sqrt{ \boxed{ \tt {4}}^{ \: \boxed{ \tt2}} \times 5} \\ &= \tt \boxed{ \tt4} \times \sqrt{5} \\ &= \tt \bf \boxed{ \bf4 }\sqrt{5} \end{aligned} \\ \\

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SOAL 8a :

\displaystyle \begin{aligned} \tt \sqrt[3]{32} &= \tt\sqrt[3]{ \boxed {\tt8} \times 4} \\ &= \tt \sqrt[3]{ \boxed{ \tt {2}}^{ \: \boxed{ \tt3}} \times 4} \\ &= \tt \boxed{ \tt2} \times \sqrt[3]{4} \\ &= \boxed{ \bf2\sqrt[3]{4}} \end{aligned}

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SOAL 8b :

\displaystyle \begin{aligned} \tt \sqrt[3]{54} &= \tt\sqrt[3]{ \boxed {\tt27} \times 2} \\ &= \tt \sqrt[3]{ \boxed{ \tt {3}}^{ \: \boxed{ \tt3}} \times 2} \\ &= \tt \boxed{ \tt3} \times \sqrt[3]{2} \\ &= \boxed{ \bf3\sqrt[3]{2}} \end{aligned} \\ \\

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SOAL 9a :

\displaystyle \tt \sqrt{ {5}^{3} } = { \boxed{ \bf5}}^{ \bf \frac{ \boxed{ \tiny \bf3}}{2} }

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SOAL 9b :

\displaystyle \tt \sqrt[3]{6 {a}^{2} } = { \boxed{ \bf6}}^{ \bf \frac{ \boxed{ \tiny \bf1}}{3} } { \boxed{ \bf a}}^{ \bf \frac{ \boxed{ \tiny \bf2}}{3} }

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SOAL 9c :

\displaystyle \tt \frac{1}{ \sqrt[4]{ {k}^{3} } } = \frac{1}{ {k}^{ \frac{ \boxed{ \tiny \tt3}}{ \boxed{ \tiny \tt4}} } } = \bf {k}^{ - \frac{ \boxed{ \tiny \bf3}}{ \boxed{ \tiny \bf4}}}

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SOAL 9d :

\displaystyle \tt \frac{4}{ \sqrt[5]{ {xy}^{3} } } = \frac{4}{ {x}^{ \frac{ \tiny \boxed{ \tt1}}{ \tiny \boxed{ \tt5}}} {y}^{ \frac{ \tiny \boxed{ \tt3}}{ \tiny \boxed{ \tt5}} } } = \bf 4 {x}^{ - \frac{ \tiny \boxed{ \bf1}}{ \tiny \boxed{ \bf5}}} {y}^{ - \frac{ \tiny \boxed{ \bf3}}{ \tiny \boxed{ \bf5}}} \\ \\

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SOAL 10a :

\displaystyle \tt {7}^{ \frac{3}{4} } = \bf \sqrt[4]{ { \boxed{ \bf7}}^{ \: \boxed{ \bf3}} }

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SOAL 10b :

\displaystyle \tt {4}^{ - \frac{2}{5} } = \bf \frac{1}{ \sqrt[5]{ { \boxed{ \bf4}}^{~ \boxed{ \bf2}} } }

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SOAL 10c :

\displaystyle \tt { - x}^{4 \frac{2}{3} } = \bf { - x}^{ \boxed{ \bf4}} \sqrt[ \boxed{ \bf3}]{ {x}^{ \boxed{ \bf2}} }

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SOAL 10d :

\displaystyle \begin{aligned} \tt {x}^{ \frac{1}{3} } {y}^{ - \frac{4}{5} } &= \tt \sqrt[ \boxed{ \tt3}]{x} \: \times \: \frac{1}{ \sqrt[ \boxed{ \tt5}]{ {y}^{ \boxed{ \tt4}} } } \\ &= \bf \frac{ \sqrt[ \boxed{ \bf3}]{x} }{\sqrt[ \boxed{ \bf5}]{ {y}^{ \boxed{ \bf4}} } } \end{aligned}

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Last Update: Tue, 18 Oct 22
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