Rational Exponents and Radicals

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 radical expression to an exponential form?

Back

To convert a radical expression to exponential form, use the formula: n√(a) = a^(1/n). For example, ∛(x) = x^(1/3).

Front

Simplify: (x^(2/3))^4

Back

x^(8/3) (Multiply the exponents: 2/3 * 4 = 8/3).

Front

What is the product of powers property?

Back

The product of powers property states that when multiplying two expressions with the same base, you add the exponents: a^m * a^n = a^(m+n).

Front

Simplify: (4^(1/3))(4^(4/3))

Back

4^(5/3) (Add the exponents: 1/3 + 4/3 = 5/3).

Front

What is the quotient of powers property?

Back

The quotient of powers property states that when dividing two expressions with the same base, you subtract the exponents: a^m / a^n = a^(m-n).

Front

Simplify: (6^(3/4))^(1/3)

Back

6^(1/4) (Multiply the exponents: 3/4 * 1/3 = 1/4).

Front

How do you express a radical in terms of rational exponents?

Back

To express a radical in terms of rational exponents, use the formula: n√(a) = a^(1/n). For example, √(x) = x^(1/2).

Front

What is the power of a power property?

Back

The power of a power property states that when raising a power to another power, you multiply the exponents: (a^m)^n = a^(m*n).

Front

Write in exponential form: ∛(x^7)

Back

x^(7/3) (Convert the radical to exponential form using the formula for roots).