This exact question is on a puzzle worksheet over rational exponents used by teachers. The answer to the puzzle is Nicole Oresme.
The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
You can use any number - rational or otherwise - as an exponent.
In terms of mathematical concepts, there is no difference at all. In practical terms, some rational exponents or rational number will result in rational answers while radical exponent won't. But that is hardly a significant difference.
YES
Radical and rational exponents both represent the same mathematical concepts of roots and fractional powers. For instance, a radical expression like (\sqrt{a}) can be expressed as a rational exponent, (a^{1/2}). Both forms can be used interchangeably in calculations, and they follow the same rules of exponents, such as multiplication and division. Additionally, both types of exponents can be applied to real numbers, allowing for similar manipulations and simplifications in algebraic expressions.
A rational exponent is an exponent in the form of a fraction. Many financial formulas use rational exponents. Compound interest is formula that uses rational exponents.
The laws of exponents work the same with rational exponents, the difference being they use fractions not integers.
You can use any number - rational or otherwise - as an exponent.
What Is an Exponent, Anyway? There
In terms of mathematical concepts, there is no difference at all. In practical terms, some rational exponents or rational number will result in rational answers while radical exponent won't. But that is hardly a significant difference.
That they can have any value: integer, rational, irrational or complex.
YES
Radical and rational exponents both represent the same mathematical concepts of roots and fractional powers. For instance, a radical expression like (\sqrt{a}) can be expressed as a rational exponent, (a^{1/2}). Both forms can be used interchangeably in calculations, and they follow the same rules of exponents, such as multiplication and division. Additionally, both types of exponents can be applied to real numbers, allowing for similar manipulations and simplifications in algebraic expressions.
A rational exponent means that you use a fraction as an exponent, for example, 10 to the power 1/3. These exponents are interpreted as follows, for example:10 to the power 1/3 = 3rd root of 1010 to the power 2/3 = (3rd root of 10) squared, or equivalently, 3rd root of (10 squared)
She has powers and roots
All the powers and exponents of 1 are 1.The powers and exponents of any of the other numbers up to 10 are equivalent to the all the positive numbers - rational and irrational.
i dont know i am asking you