Question

~QUIZ~
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Soal:
Nilai p yang memenuhi persamaan [tex]\frac{\sqrt[3]{x^{p}\sqrt{x} } }{x} = x^{p}[/tex] adalah . . . ?
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Syarat untuk menjawab soal :
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● Dilarang copas jawaban dari google.
● Jawabannya harus disertai dengan penjelasan yang masuk akal.
● Gunakanlah kata-kata jawabanmu sendiri yang baik dan benar.

Answer 1

Verified answer

Jawaban:

-5/4

Penjelasan dengan langkah-langkah:

[tex]\frac{\sqrt[3]{x^{p}\sqrt{x} } }{x} = x^{p} \\ \\ \frac{ {x}^{ \frac{p + \frac{1}{2} }{3} } }{x} = {x}^{p} \\ {x}^{ \frac{p + \frac{1}{2} }{3} } \div {x}^{1} = {x}^{p} \\ \\ \boxed{{a}^{m} \div {a}^{n} = {a}^{m - 1} } \\ {x}^{ \frac{p + \frac{1}{2} }{3} - 1 } = {x}^{p} \\ \cancel{x}^{ \frac{p + \frac{1}{2} }{3} - \frac{3}{3} } = \cancel{x}^{p} \\ p = \frac{p + \frac{1}{2} }{3} - \frac{3}{3} \\ p = \frac{2p + 1}{6} - \frac{6}{6} \\ p = \frac{2p - 5}{6} \\ 6p = 2p - 5 \\ 6p - 2p = - 5 \\ 4p = - 5 \\ p = - \frac{ 5}{4} [/tex]

Answer 2

[tex]\displaystyle\bf~ p = - \frac{ 5}{4} [/tex]

Penjelasan dengan langkah-langkah:

[tex]\displaystyle\bf~\frac{\sqrt[3]{x^{p}\sqrt{x} } }{x} = x^{p} \\ \\ \displaystyle\bf~ \frac{ \sqrt[3]{ {x}^{p}. {x}^{ \frac{1}{2} } } }{x} = {x}^{p} \\ \\ \displaystyle\bf~ \frac{ {( {x}^{p} . {x}^{ \frac{1}{2} } })^{ \frac{1}{3} } }{x} = {x}^{p} \\ \\ \displaystyle\bf~ \frac{ {x}^{ \frac{p}{3} } . {x}^{ \frac{1}{6} } }{x} = {x}^{p} \\ \displaystyle\bf~ {x}^{ \frac{p}{3} + \frac{1}{6} - 1 } = {x}^{p} \\ \\ \displaystyle\bf~ \frac{p}{3} + \frac{1}{6} - 1 = p \\ \\ \displaystyle\bf~ \frac{p}{3} + \frac{1}{6} - \frac{6}{6} = p \\ \\ \displaystyle\bf~ \frac{p}{3} - \frac{5}{6} = p \\ \\ \displaystyle\bf~ \frac{p}{3} - p = \frac{5}{6} \\ \\ \displaystyle\bf~ \frac{p}{3} - \frac{3p}{3} = \frac{5}{6} \\ \\ \displaystyle\bf~ \frac{ - 2p}{3} = \frac{5}{6} \\ \\ \displaystyle\bf~ - 12p = 15 \\ \\ \displaystyle\bf~p = \frac{15}{ - 12} \\ \\ \displaystyle\bf~p = - \frac{5}{4} [/tex]

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