To fill: The correct expression in the box for each equation An eq

druczekq4 2021-11-12 Answered
To fill: The correct expression in the box for each equation
An equation: \(\displaystyle\underline{{\ }}\cdot{x}^{{{\frac{{{1}}}{{{8}}}}}}={x}^{{{\frac{{{4}}}{{{8}}}}}}\), or \(\displaystyle{x}^{{{\frac{{{1}}}{{{2}}}}}}\)

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Expert Answer

Howell
Answered 2021-11-13 Author has 9766 answers
Step 1
Let us find the expression for given blank as shown below:
\(\displaystyle\underline{{\ }}\cdot{x}^{{{\frac{{{1}}}{{{8}}}}}}={x}^{{{\frac{{{4}}}{{{8}}}}}}\) (Given expression)
\(\displaystyle\underline{{\ }}\cdot{\frac{{{x}^{{{\frac{{{1}}}{{{8}}}}}}}}{{{x}^{{{\frac{{{1}}}{{{8}}}}}}}}}={\frac{{{x}^{{{\frac{{{4}}}{{{8}}}}}}}}{{{x}^{{{\frac{{{1}}}{{{8}}}}}}}}}\) (Divide both sides by \(\displaystyle{x}^{{{\frac{{{1}}}{{{8}}}}}}\)
\(\displaystyle\Rightarrow\underline{{\ }}={\frac{{{x}^{{{\frac{{{4}}}{{{8}}}}}}}}{{{x}^{{{\frac{{{1}}}{{{8}}}}}}}}}\)
\(\displaystyle\Rightarrow\underline{{\ }}={x}^{{{\frac{{{4}}}{{{8}}}}-{\frac{{{1}}}{{{8}}}}}}\) (Applying rule \(\displaystyle{\frac{{{a}^{{{m}}}}}{{{a}^{{{n}}}}}}={a}^{{{m}-{n}}}\))
\(\displaystyle\Rightarrow\underline{{\ }}={x}^{{{\frac{{{3}}}{{{8}}}}}}\)
Therefore, the expression for the given blank would be \(\displaystyle{x}^{{{\frac{{{3}}}{{{8}}}}}}\)
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