Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) is the square root of x.

Front

How do you convert a rational exponent to a radical expression?

Back

To convert a rational exponent to a radical expression, use the formula: x^(m/n) = n√(x^m), where m is the power and n is the root.

Front

What is the relationship between square roots and rational exponents?

Back

The square root of a number can be expressed as a rational exponent: √x = x^(1/2).

Front

How do you express x^(1/n) using a radical?

Back

x^(1/n) can be expressed as the nth root of x, written as n√x.

Front

What is the value of x^(0)?

Back

For any non-zero number x, x^(0) = 1.

Front

What is the value of x^(1)?

Back

For any number x, x^(1) = x.

Front

How do you simplify x^(m/n) when m and n are integers?

Back

To simplify x^(m/n), express it as n√(x^m) or (x^m)^(1/n).

Front

What is the formula for converting a radical expression to a rational exponent?

Back

The formula is: n√(x^m) = x^(m/n).

Front

How do you express the cube root of x^8 using a rational exponent?

Back

The cube root of x^8 can be expressed as x^(8/3).

Front

What is the general form of a radical expression?

Back

The general form of a radical expression is n√(x^m), where n is the index and m is the exponent.