Converting Radical forms

Front

What is the exponential form of a radical expression?

Back

A radical expression can be written in exponential form by using the formula: √(a) = a^(1/2) for square roots, and √[n](a) = a^(1/n) for nth roots.

Front

How do you convert a radical expression to exponential form?

Back

To convert a radical expression to exponential form, identify the index of the root and express it as a fractional exponent. For example, √(x) = x^(1/2) and ∛(x) = x^(1/3).

Front

What is the root index in the expression 12x^(5/8) when rewritten in radical form?

Back

The root index is 8, as the expression can be rewritten as the 8th root of (12x^5).

Front

Convert the expression √(x^4) to exponential form.

Back

The exponential form is x^(4/2) = x^2.

Front

What is the relationship between radical and exponential forms?

Back

Radical forms and exponential forms are two ways to express the same mathematical concept. The radical form uses roots, while the exponential form uses fractional exponents.

Front

Convert the expression ∛(27) to exponential form.

Back

The exponential form is 27^(1/3).

Front

What is the exponential form of the expression √[5](x^3)?

Back

The exponential form is x^(3/5).

Front

How do you simplify the expression √(x^6)?

Back

The simplified form is x^(6/2) = x^3.

Front

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

Back

The value is √(2^3) = √8 = 2√2.

Front

Convert the expression 4√(x^2) to exponential form.

Back

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