Rewriting Radical and Rational Exponents

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, √x is a radical expression.

Front

How do you rewrite a radical expression in exponential form?

Back

To rewrite a radical expression in exponential form, use the formula: √a = a^(1/2), ∛a = a^(1/3), etc.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed as radicals. For example, a^(m/n) = n√(a^m).

Front

What is the value of 7^(1/2)?

Back

7^(1/2) is equal to √7.

Front

How do you convert 7^(3/4) to radical form?

Back

7^(3/4) can be rewritten as the fourth root of 7 cubed: 4√(7^3).

Front

What does the expression x^(1/n) represent?

Back

The expression x^(1/n) represents the nth root of x.

Front

What is the value of 16^(3/4)?

Back

16^(3/4) = 4^3 = 64.

Front

How do you simplify the expression (x^(1/2))^2?

Back

Using the power of a power property, (x^(1/2))^2 = x^(1/2 * 2) = x^1 = x.

Front

What is the definition of 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 express the cube root of x in exponential form?

Back

The cube root of x can be expressed as x^(1/3).