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gulaghasi [49]
3 years ago
15

Which of the following represents 6 x to the 3 fourths power in radical form?

Mathematics
2 answers:
kotegsom [21]3 years ago
7 0

Answer:

\\ 6x^{\frac{3}{4}} = 6\sqrt[4]{x^{3}}

Step-by-step explanation:

When a number is raised to a <em>rational</em> number like \\ {\frac{3}{4}}, that is, a fraction, the <em>denominator</em> represents the <em>index</em> of the radical (or commonly known as the root nth of the radical), and the <em>numerator</em> represents the number to which the radicand (the part of the expression inside the radical sign) is about to be raised.

Looking at \\ 6x^{\frac{3}{4}}, the <em>index</em> (root) of the radical is 4 and the numerator raises the value of x to the third power, that is,  \\ x^{3}. That explains the answer: six (6) times \\ \sqrt[4]{x^{3}}. The six (6) only multiplies the expression.

Likewise, a radical of index 5, with a radicand \\ (x + 8) raised to the ninth power is represented by  \\ \sqrt[5]{(x + 8)^{9}}, which is equivalent to \\ (x+8)^{\frac{9}{5}}.

By the way, a particular case is when the index is 2, that is, \\ x^{\frac{1}{2}}. Here, the number <em>2</em> is omitted from the radical symbol and is represented by \sqrt{x}.

lukranit [14]3 years ago
4 0
6 √x^3 - I am not sure how to write 4th root on the computer but the answer is 6 times the 4th root of x to the 3 third power. 
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