Simplify Rational Exponents

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 simplify a negative rational exponent?

Back

To simplify a negative rational exponent, take the reciprocal of the base raised to the positive exponent.

Front

What is the value of (81/625)^(-5/4)?

Back

3125/243

Front

If 64^x = 512, what is x?

Back

3/2

Front

How do you simplify 64^(-3/2)?

Back

The result is 1/512.

Front

What is the value of (1728)^(2/3)?

Back

144

Front

How do you calculate 8^(3/2)?

Back

The result is 16.

Front

What does the expression a^(m/n) represent?

Back

It represents the n-th root of a raised to the m-th power.

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be expressed as roots; for example, a^(1/n) is the n-th root of a.

Front

How do you convert a rational exponent to radical form?

Back

a^(m/n) = n√(a^m).