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 an expression with a zero exponent?

Back

Any non-zero base raised to the power of zero equals 1.

Front

Convert the expression x^{3/4} into radical form.

Back

x^{3/4} = \sqrt[4]{x^3}.

Front

What is the result of any number raised to the power of zero?

Back

The result is 1, provided the base is not zero.

Front

How do you simplify an expression with a negative exponent?

Back

A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent.

Front

What is the simplified form of (x^{5/3}y^{-2})^0?

Back

1.

Front

How do you express x^{-9/4} in terms of positive exponents?

Back

x^{-9/4} = \frac{1}{x^{9/4}}.

Front

What is the simplified form of (x^0y^{1/3})^{3/2}x^0?

Back

y^{1/2}.

Front

What does the expression \sqrt[4]{x^3} represent?

Back

It represents x raised to the power of 3 divided by 4.

Front

If x = 2, what is the value of 2^{3/4}?

Back

2^{3/4} = \sqrt[4]{2^3} = \sqrt[4]{8}.