How to write a radical in exponential form?
Understand the Problem
The question is asking how to express a radical (a root expression) using exponent notation. This concept involves understanding the relationship between roots and fractional exponents.
Answer
The radical expression $$ \sqrt[n]{a} $$ is expressed as $$ a^{\frac{1}{n}} $$.
Answer for screen readers
The radical expression $$ \sqrt[n]{a} $$ can be expressed using exponent notation as $$ a^{\frac{1}{n}} $$.
Steps to Solve
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Identify the radical expression
Let's say we have a radical expression of the form $$ \sqrt[n]{a} $$, where ( n ) is the index of the root and ( a ) is the number under the radical. -
Convert the radical to exponent form
We apply the rule that relates radicals to exponents:
$$ \sqrt[n]{a} = a^{1/n} $$
This means the ( n )-th root of ( a ) is equivalent to ( a ) raised to the power of ( \frac{1}{n} ). -
Example conversion
For example, if we have $$ \sqrt{16} $$, it can be expressed as:
$$ \sqrt{16} = 16^{1/2} $$
Alternatively, for a cube root, $$ \sqrt[3]{8} $$ can be expressed as:
$$ \sqrt[3]{8} = 8^{1/3} $$ -
Final expression
To summarize, any radical expression $$ \sqrt[n]{a} $$ can be rewritten in the exponent notation as:
$$ \sqrt[n]{a} = a^{1/n} $$
The radical expression $$ \sqrt[n]{a} $$ can be expressed using exponent notation as $$ a^{\frac{1}{n}} $$.
More Information
This conversion is a critical concept in mathematics, bridging the gap between root expressions and exponent notation. Understanding this relationship helps simplify calculations and solve equations involving radicals more easily.
Tips
- Misidentifying the index: Make sure to correctly identify the index of the radical before converting.
- Forgetting to use the reciprocal: Remember that the ( n )-th root corresponds to raising to the power of ( \frac{1}{n} ), not ( n ).
