Simplifying Rational Exponents

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.

Front

Simplify: 2^(3/2)

Back

2^(3/2) = √(2^3) = √8 = 2√2.

Front

What is the relationship between rational exponents and radicals?

Back

Rational exponents can be expressed in radical form, where a^(m/n) = n√(a^m).

Front

Simplify: 9^(1/2)

Back

9^(1/2) = √9 = 3.

Front

Convert the expression 16^(3/4) to radical form.

Back

16^(3/4) = 4√(16^3) = 4√(4096) = 64.

Front

What does the expression a^(m/n) represent?

Back

a^(m/n) represents the n-th root of a raised to the m-th power.

Front

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

Back

(x^2)^(3/4) = x^(2*3/4) = x^(3/2).

Front

Convert 27^(2/3) to radical form.

Back

27^(2/3) = 3√(27^2) = 3√729 = 9.

Front

What is the value of 4^(5/2)?

Back

4^(5/2) = (√4)^5 = 2^5 = 32.

Front

Rewrite the expression without using a radical: (3x+2)^(1/3)

Back

(3x+2)^(1/3) = 3√(3x+2).