Sophia __ COLLEGE ALGEBRA UNIT 1MILESTONE

Score 16/21 You passed this Milestone 16 questions were answered correctly. 5UquNestiIonTs we1re a—nswerMed inIcLorrEectSly.TONE 1 Simplify the following expression in terms of fractional exponents and write it in the form . RATIONALE Radical expressions can be rewritten using fractional exponents by corresponding the index of the radical to the denominator of the fractional exponent. Begin by writing the expression underneath the radical. This entire expression will be raised to a fractional exponent power. The index of the radical is . In other words, this is the fourth-root. This means that the entire expression will be raised to the power of . Next, to write this in the form 10 to the power of a x to the power of b, distribute the outside exponent of to the powers of and x. Once the exponent of is distributed to both terms, we can simplify by multiplying the exponents and for the term of 10. In this case, becomes . The final expression is . CONCEPT Fractional Exponents and Radicals 2 Perform the following operations and write the result as a single number. RATIONALE Following the Order of Operations, we must first evaluate everything in parentheses and grouping symbols. When there are brackets or braces, evaluate the innermost operations first. Here, we must evaluate 5 minus 3 first. 5 minus 3 is 2. There are still operations inside grouping symbols to evaluate. Multiplication comes before addition, so we must evaluate 8 times 2 next. 8 times 2 is 16. Next, we add 4 and 16 to complete the operations inside parentheses. 4 plus 16 is 20. Now there is just division and subtraction. Division comes before subtraction in the Order of Operations, so we divide 20 by 5 next. 20 divided by 5 is 4. Lastly, add 4 and 6. 4 plus 6 is 10. CONCEPT Introduction to Order of Operations 3 Simplify the following radical expression. RATIONALE To simplify this expression, we can rewrite into products of smaller numbers. There are many ways to do this, but it can help to use a perfect square, since they simplify to integers when we evaluate the square root. can be written as times . Now we can use the Product Property of Radicals to write the factors as separate radicals. The Product Property allows us to write the radical as the product of individual roots. Finally, we can evaluate the square roots. The square root of 9 is 3. The square root of 5 is already written in its simplest form. The fully simplified radical is CONCEPT Simplifying Radical Expressions 4 Write the expression as a single power of b. This study source was downloaded by from CourseH on :17:02 GMT -05:00 RATIONALE Start by simplifying the terms in the parentheses. Using the Quotient Property of Exponents, divide the two terms that have the same base by subtracting the exponents, and 1 fourth. When subtracting fractions with a common denominator, subtract across the numerators and leave the denominator the same. minus equals . Next, apply the Power of Property of Exponents to multiply the two exponents and write as a single power. times equals . Lastly, rewrite the fraction in its simplest form. can simplify to , so the expression simplifies to . CONCEPT Properties of Fractional and Negative Exponents 5 What is the value of the following expression? RATIONALE To solve this expression, evaluate the exponent for each term. Start with the first term, . Any number taken to the power of zero equals , so is equal to . Evaluate the next term, . When the exponent is , the value of the term is the same as its base, so to the first power is . Next, evaluate the term , which is the same as . Negative times negative equals positive . The last term, indicates that is multiplied by itself three times. equals , because when a negative number is multiplied by itself an odd number of times, the answer remains negative. Finally, add all of the terms. CONCEPT ....................................continued..............................