jika a = 1/9, b = 8, dan c = 125, hitunglah :a.[tex] {a}^{0}b ^{ \frac{1}{3} } c^{ \frac{2}{3} } [/t.... Question from @ijklmnoabcdefgh12

Gusti2601

$\mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}$

$\begin{aligned} &&\begin{aligned} \bf{a. \: } \boxed{ \: \bf{50} \: } \end{aligned} \end{aligned}$

$\begin{aligned} &&\begin{aligned} \bf{b. \: } \boxed{ \: \bf{7 \frac{1}{3} } \: } \end{aligned} \end{aligned}$

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

$\underline{ \overline{ \boxed{ \bold{diketahui}}}}$

a = $\tt{ \frac{1}{9} }$
b = 8
c = 125

$\\ \underline{ \overline{ \boxed{ \bold{ditanya}}}}$

$\sf{a) \: {a}^{0} {b}^{ \frac{1}{3} } {c}^{ \frac{2}{3} } }$
$\sf{b) \: {a}^{ \frac{1}{2} } + {b}^{ \frac{1}{3} } + {c}^{ \frac{1}{3} } }$

$\\ \underline{ \overline{ \boxed{ \bold{jawab}}}}$

SOAL a :

$\begin{aligned} &\begin{aligned} \end{aligned}\small{ \blue{ \bf{Gunakan \: sifat - sifat \: eksponen \: berikut : }}} \\ &\boxed{ \: \begin{aligned} \tt{ {a}^{0} } &= \tt{1} \\ \tt{ {( {a}^{m} )}^{n} } &= \tt{ {a}^{m \times n} } \end{aligned} \: } \end{aligned} \\ \\$

$\boxed{ \: \begin{aligned} \tt{{a}^{0} {b}^{ \frac{1}{3} } {c}^{ \frac{2}{3} }} &= \tt{ {a}^{0} \cdot {b}^{ \frac{1}{3} } \cdot {c}^{ \frac{2}{3} }} \\ &= \tt{1 \cdot {8}^{ \frac{1}{3} } \cdot {125}^{ \frac{2}{3} } } \\ &= \tt{1 \cdot {( {2}^{ \not{3}} )}^{ \frac{1}{ \not{3}} } \cdot {( {5}^{ \not{3}} )}^{ \frac{2}{ \not{3}} } } \\ &= \tt{1 \cdot {2}^{1} \cdot {5}^{2} } \\ &= \tt{1 \cdot2 \cdot25} \\ &= \red{ \boxed{ \bf{ \green{50}}}} \end{aligned} \: } \\ \\$

SOAL b :

$\begin{aligned} &\begin{aligned} \end{aligned}\small{ \blue{ \bf{Gunakan \: sifat - sifat \: eksponen \: berikut : }}} \\ &\boxed{ \: \begin{aligned} \tt{ {( {a}^{m} )}^{n} } &= \tt{ {a}^{m \times n} } \\ \tt{ {a}^{ - n} } &= \small{\tt{ \frac{1}{ {a}^{n} } }} \end{aligned} \: } \end{aligned} \\ \\$

$\boxed{ \: \begin{aligned} \tt{{a}^{ \frac{1}{2} } + {b}^{ \frac{1}{3} } + {c}^{ \frac{1}{3} }} &= \tt{{ \left( \frac{1}{9} \right)}^{ \frac{1}{2} } + {8}^{ \frac{1}{3} } + {125}^{ \frac{1}{3} } } \\ &= \tt{{ \left( \frac{1}{ {3}^{2} } \right)}^{ \frac{1}{2} } + {( {2}^{ \not{3}})}^{ \frac{1}{ \not{3}} } + {( {5}^{ \not{3}} )}^{ \frac{1}{ \not{3}} } } \\ &= \tt{{( {3}^{ - \not{2}} ) }^{ \frac{1}{ \not{2}} } + {2}^{1} + {5}^{1} } \\ &= \tt{ {3}^{ - 1} + 2 + 5} \\ &= \tt{ \frac{1}{3} + 2 + 5} \\ &= \red{ \boxed{ \bf{ \green{7 \frac{1}{3} }}}} \end{aligned} \: }$

$\colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{}$

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SOAL a :

SOAL b :

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