Alg. 2: 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. For example, p^(2/3) means the cube root of p squared.

Front

How do you convert a rational exponent to radical form?

Back

To convert a rational exponent to radical form, use the formula a^(m/n) = n√(a^m), where m is the numerator and n is the denominator.

Front

What is the value of p^(2/3) when p = 8?

Back

p^(2/3) = 8^(2/3) = (∛8)^2 = 2^2 = 4.

Front

Which expression is equivalent to (x^(2/3))^4?

Back

(x^(2/3))^4 = x^(8/3).

Front

What is the simplified form of x^(-1/2) * x^(-1/4)?

Back

x^(-1/2) * x^(-1/4) = x^(-1/2 - 1/4) = x^(-3/4) = 1/x^(3/4).

Front

How do you simplify (x^(2/3))^(2/5)?

Back

(x^(2/3))^(2/5) = x^(2/3 * 2/5) = x^(4/15).

Front

What is the relationship between x^(1/2) and √x?

Back

x^(1/2) is equivalent to √x, as the exponent 1/2 represents the square root.

Front

If x^(1/3) = 2, what is the value of x?

Back

To find x, cube both sides: x = 2^3 = 8.

Front

What is the value of (p^(1/3))^3?

Back

The value is p, since raising to the power of 3 cancels the cube root.

Front

How do you express √(x^3) in terms of rational exponents?

Back

√(x^3) can be expressed as x^(3/2).