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.

Tags

CCSS.HSN.RN.A.2

Front

How do you express a square root in exponential form?

Back

The square root of a number 'x' can be expressed as x^(1/2).

Tags

CCSS.HSN.RN.A.2

Front

How do you express a cube root in exponential form?

Back

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

Front

What is the relationship between rational exponents and roots?

Back

Rational exponents can be used to represent roots; for example, x^(m/n) represents the n-th root of x raised to the m-th power.

Tags

CCSS.HSN.RN.A.2

Front

Convert the expression ∛x⁷ to exponential form.

Back

x^(7/3).

Front

Convert the expression x^(5/3) to radical form.

Back

∛(x^5).

Front

What is the value of x^(1/4) when x = 16?

Back

2, because 16^(1/4) = 2.

Front

Simplify the expression x^(3/2) * x^(1/2).

Back

x^(3/2 + 1/2) = x^(4/2) = x^2.

Front

What is the result of (x^(1/3))^3?

Back

x^(1/3 * 3) = x^1 = x.

Front

Rewrite the expression x^(2/5) in radical form.

Back

The expression can be rewritten as the fifth root of x squared: ∛(x^2).