PROPERTIES OF RATIONAL EXPONENTS 1 Section 7.2

7.2 – Properties of Rational Exponents Simplifying Expressions Containing Rational Exponents: Laws of Exponents: For any integers m, n (assuming no divisions by 0) new! and Recognize these?!?!

3 7.2 – Properties of Rational Exponents

Properties of Exponents Applied to Radicals: Simplifying Radicals: A radical is in simplest form when…  No radicals appear in the denominator of a fraction  The radicand cannot have any factors that are perfect roots (given the index) Examples: Simplify each expression. 7.2 – Properties of Rational Exponents

Simplifying Radical Expressions Containing Variables: Examples: Simplify each expression. Assume that all variables are positive. When we divide the exponent by the index, the remainder remains under the radical 7.2 – Properties of Rational Exponents

Multiplying and Dividing Radical Expressions: Examples: Simplify each expression. Assume that all variables are positive. 7.2 – Properties of Rational Exponents

Rationalizing Denominators: Recall that simplifying a radical expression means that no radicals appear in the denominator of a fraction. Examples: Simplify each expression. Assume that all variables are positive. 7.2 – Properties of Rational Exponents

Adding and Subtracting Radical Expressions:  simplify each radical expression  combine all like-radicals (combine the coefficients and keep the common radical) Examples: Simplify each expression. Assume that all variables are positive. 7.2 – Properties of Rational Exponents

Examples: Simplify each expression. Express your answer so that only positive exponents occur. Assume that the variables are positive. 7.2 – Properties of Rational Exponents

Examples: Simplify each expression. Assume that all variables are positive. 7.2 – Properties of Rational Exponents

Example: The final velocity, v, of an object in feet per second (ft/sec) after it slides down a frictionless inclined plane of height h feet is: where is the initial velocity in ft/sec of the object. What is the final velocity, v, of an object that slides down a frictionless inclined plane of height 2 feet with an initial velocity of 4 ft/sec? 7.2 – Properties of Rational Exponents

Homework: Homework: pgs #22-28 even, 34-36, 42, 44, 50, 52, 56, – Properties of Rational Exponents

From Math for Artists… “These are the laws of exponents and radicals in bright, cheerful, easy to memorize colors.” 7.2 – Properties of Rational Exponents