Laws of Exponents with Rational Exponents
Key points
- Rational exponents are those which are a fractional.
- They can be converted to radical expressions.
- Exponents for rational expressions have their own set of laws.
Rational Exponents are exponents which are expressed as fractions. They may contain variables, or may be just integers.
- Rational exponents can be expressed in radical expression.
- The numerator becomes the exponent on the radicand.
- The denominator becomes the index of the radical expression.
- For example, x to the power of 1/2 is equivalent to the square root of x.
Rational expressions may be elevated to a certain exponent or power. This comes with its own set of laws.
- If a radical expression is elevated to a power, the exponent is distributed to both the numerator and the denominator.
- Anything with a negative exponent becomes a denominator.
- A whole fraction elevated to a negative power means you take the reciprocal.
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