Q#3 Radicals and Rational Exponentss

Front

Define a radical expression.

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

What is a rational exponent?

Back

Front

Simplify the expression: @@rac{1}{ oot{3}{x^6}}@@.

Back

@@rac{1}{ oot{3}{x^6}} = rac{1}{x^2}$$.

Front

What is the product rule for radicals?

Back

The product rule states that @@ oot{n}{a} imes oot{n}{b} = oot{n}{a imes b}@@.

Front

Simplify the expression: @@ oot{4}{x^8}@@.

Back

@@ oot{4}{x^8} = x^2$$.

Front

What is the quotient rule for radicals?

Back

The quotient rule states that @@rac{ oot{n}{a}}{ oot{n}{b}} = oot{n}{rac{a}{b}}@@.

Front

Simplify the expression: @@ oot{3}{27}@@.

Back

@@ oot{3}{27} = 3$$.

Front

What is the relationship between radicals and rational exponents?

Back

Radicals can be expressed as rational exponents. For example, @@ oot{n}{x} = x^{rac{1}{n}}@@.

Front

Simplify the expression: @@ oot{2}{50} - oot{2}{18}@@.

Back

@@ oot{2}{50} - oot{2}{18} = oot{2}{32} = 4 oot{2}$$.

Front

What is the power rule for radicals?

Back

The power rule states that @@ oot{n}{a^m} = a^{rac{m}{n}}@@.