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

Simplify: (81/625)^(-5/4)

Back

3125/243

Front

Simplify: 64^(-3/2)

Back

1/512

Front

If 343^x = 49, what is x?

Back

2/3

Front

Simplify: 216^(2/3)

Back

36

Front

What is the value of (-1)^(1/2)?

Back

i (the imaginary unit)

Front

How do you convert a negative exponent to a positive exponent?

Back

To convert a negative exponent to a positive exponent, take the reciprocal of the base raised to the absolute value of the exponent.

Front

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

Back

a^(m/n) represents the n-th root of a raised to the m-th power.

Front

Simplify: (16)^(3/4)

Back

8

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.