Rational Exponents and Radicals

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, where the numerator indicates the power and the denominator indicates the root.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent a^(m/n) to radical form, write it as the n-th root of a raised to the m-th power: a^(m/n) = n√(a^m).

Front

What is the base in the expression (-2)^(1/3)?

Back

The base is -2.

Front

What is the simplified form of (x^(1/2))^2?

Back

The simplified form is x.

Front

How do you express the square root of a number in exponential form?

Back

The square root of a number a can be expressed in exponential form as a^(1/2).

Front

What is the result of (6^(3/4))^(1/3)?

Back

The result is 6^(1/4).

Front

What does it mean to simplify an expression with exponents?

Back

Simplifying an expression with exponents means to rewrite it in a more compact or standard form, often using positive exponents.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent both powers and roots; the denominator of the exponent indicates the root, while the numerator indicates the power.

Front

How do you rewrite the expression √23 in exponential form?

Back

The expression √23 can be rewritten in exponential form as 23^(1/2).

Front

What is the rule for multiplying powers with the same base?

Back

When multiplying powers with the same base, you add the exponents: a^m * a^n = a^(m+n).