Rational/Fractional 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, x^(1/2) is the square root of x.

Front

How do you convert a fractional exponent to a radical expression?

Back

To convert a fractional exponent to a radical expression, use the formula: a^(m/n) = n√(a^m). For example, x^(3/2) = √(x^3).

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents represent roots. For example, x^(1/n) represents the nth root of x.

Front

Which expression represents the cube root of y?

Back

y^(1/3) or ∛y.

Front

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

Back

x^(2/3) can be simplified to (∛x)^2.

Front

What is the value of 8^(1/3)?

Back

The value of 8^(1/3) is 2, since 2^3 = 8.

Front

How do you express √(x^4) using exponents?

Back

√(x^4) can be expressed as x^(4/2) = x^2.

Front

What is the result of (x^(1/2))^4?

Back

The result is x^(1/2 * 4) = x^2.

Front

If a^(m/n) = b, how can you express b in terms of a?

Back

b = n√(a^m).

Front

What is the simplified form of 27^(2/3)?

Back

27^(2/3) = (3^3)^(2/3) = 3^2 = 9.