Question

Q. Chii`
[tex] \sf \frac{ \sqrt[4]{32} \: \times \: \sqrt{4} }{ {2}^{ - 1} } = ....[/tex]
hasilnya adalah...​

Answer 1

Verified answer

[tex]\displaystyle ~~~~~~~~~~~~~~~~\because\sqrt[c]{a^b}=a^{\frac{b}{c}} \therefore\\\\\frac{\sqrt[4]{32}\times\sqrt{4} }{2^{-1}}=\frac{\sqrt[4]{2^5}\times\sqrt{2^2} }{2^{-1}}=\frac{2^{\frac{5}{4}}\times2^1 }{2^{-1}}\\\\\because n^a\times n^b=n^{a+b},\:\:\:n^a\div n^b=n^{a-b}\therefore\\\\=\frac{2^{\frac{5}{4}+1}}{2^{-1}}=\frac{2^{\frac{5}{4}+\frac{4}{4}}}{2^{-1}}=\frac{2^{\frac{9}{4}}}{2^{-1}}=2^{\frac{9}{4}-(-1)}[/tex]
[tex]\displaystyle =2^{\frac{9}{4}+1}=2^{\frac{9}{4}+\frac{4}{4}}=2^{\frac{13}{4}}=2^{\frac{12+1}{4}}\\\\\because n^{a+b}=n^a\times n^b,\:\:\: a^{\frac{b}{c}}=\sqrt[c]{a^b} \therefore\\\\=2^{\frac{12}{4}+\frac{1}{4}}=2^{\frac{12}{4}}\times 2^{\frac{1}{4}}=2^{3}\times \sqrt[4]{2^1}\\\\=\bf 8\sqrt[4]{2}[/tex]
hasilnya adalah... 8 kali akar kuartik dari 2
(xcvi)

Answer 2

Eksponensial

..

[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]

Persoalan

[tex]\frac{ \sqrt[4]{32} \: \times \: \sqrt{4} }{ {2}^{ - 1} } = ...[/tex]

Penyelesaian Soal

[tex] \boxed{\bold{\underline{}\frac{ \sqrt[4]{32} \: \times \: \sqrt{4} }{ {2}^{ - 1} }}}[/tex]

[tex] = \frac{ \sqrt[4]{32} \sqrt{4} }{2 {}^{ - 1} } [/tex]

[tex] = \frac{ \sqrt[4]{32} \times 2 {}^{} }{2 {}^{ - 1} } [/tex]

[tex] = \sqrt[4]{32} \times 2 {}^{2} [/tex]

[tex] = 2 \sqrt[4]{2} \times 2 {}^{2} [/tex]

[tex] = 2 {}^{3} \times \sqrt[4]{2} [/tex]

[tex] = 8 \sqrt[4]{2} [/tex]

[tex]\boxed{\colorbox{ccddff}{Answered by Danial Alf'at | 29 - 07 - 2023}}[/tex]