Rational Exponents Review

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is expressed as a fraction, where the numerator indicates the power and the denominator indicates the root. For example, x^(1/2) represents the square root of x.

Front

How do you simplify the expression 3^(1/2) * 27^(1/2)?

Back

To simplify, you can combine the bases under a single square root: sqrt(3 * 27) = sqrt(81) = 9.

Front

What is the relationship between roots and rational exponents?

Back

Roots can be expressed as rational exponents. For example, the square root of x can be written as x^(1/2) and the cube root of x as x^(1/3).

Front

How can you rewrite the expression √x using a rational exponent?

Back

√x can be rewritten as x^(1/2).

Front

What is the rational exponent for the expression √[5]{x^3}?

Back

The rational exponent for √[5]{x^3} is x^(3/5).

Front

How do you express the square root of x^11 using a rational exponent?

Back

The square root of x^11 can be expressed as x^(11/2).

Front

What is the simplified form of √28?

Back

The simplified form of √28 is 2√7.

Front

What is the general formula for converting a root to a rational exponent?

Back

The general formula is: n√(a^m) = a^(m/n), where n is the root and m is the exponent.

Front

How do you simplify expressions with rational exponents?

Back

To simplify expressions with rational exponents, apply the laws of exponents, such as multiplying bases, adding exponents, and converting roots to fractional exponents.

Front

What is the value of 27^(1/2)?

Back

The value of 27^(1/2) is 3, since the square root of 27 is 3.