Rational Exponents

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a root and a power. For example, x^(1/2) is the square root of x.

Front

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

Back

To convert a rational 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 indicate roots. For example, an exponent of 1/3 indicates a cube root.

Front

Simplify: x^(1/2) * x^(1/2)

Back

x^(1/2 + 1/2) = x^1 = x.

Front

Simplify: (x^(1/3))^3

Back

x^(1/3 * 3) = x^1 = x.

Front

What is the value of 64^(1/2)?

Back

8, because the square root of 64 is 8.

Front

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

Back

9, because 27^(1/3) is 3, and 3^2 is 9.

Front

If a^(m/n) = b, what is a?

Back

a = b^(n/m), which means you can express a in terms of b and the rational exponent.

Front

What is the product rule for exponents?

Back

The product rule states that a^m * a^n = a^(m+n).

Front

What is the power rule for exponents?

Back

The power rule states that (a^m)^n = a^(m*n).