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d1i1m1o1n [39]
3 years ago
10

Which of the following is the simplified form of fifth root of x times the fifth root of x times the fifth root of x times the f

ifth root of x?
Mathematics
2 answers:
Snezhnost [94]3 years ago
7 0

Answer:

x^4/5

Step-by-step explanation:

lions [1.4K]3 years ago
4 0

<u>Answer:</u>

Simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x is \sqrt[5]{x^{4}}

<u>Solution:</u>

Need to find simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x. That is need to find simplified form of following expression.

\sqrt[5]{x} \times \sqrt[5]{x} \times \sqrt[5]{x} \times \sqrt[5]{x}

\text { since } \sqrt[n]{a}=(a)^{\frac{1}{n}} we get

=>(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}}

Now using law of exponent that is \mathrm{a}^{\mathrm{m}} \times \mathrm{a}^{\mathrm{n}}=\mathrm{a}^{\mathrm{m}+\mathrm{n}}

\begin{array}{l}{\Rightarrow(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}} \times(x)^{\frac{1}{5}}} \\\\ {=(x)^{\frac{1}{5}+\frac{1}{5}} \times(x)^{\frac{1}{5}}} \\\\ {=(x)^{\frac{2}{5}} \times(x)^{\frac{2}{5}}} \\\\ {=(x)^{\frac{2}{5}} \times(x)^{\frac{2}{5}}} \\\\ {=(x)^{\frac{2}{5} +\frac{2}{5} \\\\ {=(x)^{\frac{4}{5}}}\end{array}

Using another law of exponent that is (a)^{m \times n}=\left((a)^{m}\right)^{n} we get

\begin{array}{l}{(x)^{\frac{4}{5}}=(x)^{4 \times \frac{1}{5}}=\left((x)^{4}\right)^{\frac{1}{5}}} \\\\ {\left((x)^{4}\right)^{\frac{1}{5}}=\sqrt[5]{x^{4}}}\end{array}

Hence the simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x is \sqrt[5]{x^{4}}

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