Exponents, Square Roots, and the Order of Operations

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Exponents, Square Roots, and the Order of Operations Exponential Expressions An exponent is used to show repeated multiplication of the base. Definition of bn Let b represent any real number and n represent a positive integer. Then n factors of b For , b is called the base and n is called the exponent or power. Write in exponential form. Do not evaluate. 1. 2. 3. Write each expression in expanded form. 4. 5. Simplify each expression. 6. 7. 8. Square Roots To square a number means that we multiply the base times itself. To find a square root of a number means that we reverse the process of squaring. The symbol (called a radical sign) is used to find the principal square root of a number. By definition, the principal square root is nonnegative. Example: The square of 7 is 49. Therefore, the square root of 49 is 7. Evaluate the square roots. 9. 10. Order of Operations Applying the Order of Operations Step 1 Simplify expressions within parentheses and other grouping symbols first. These include absolute value bars, fraction bars and radicals. If embedded parentheses are present, start with the innermost parentheses. Step 2 Evaluate expressions involving exponents, radicals, and absolute values. Step 3 Perform multiplication or division in the order that they occur from left to right. Step 4 Perform addition or subtraction in the order that they occur from left to right. Simplify the expression. 11. 12. 13. 14. 15. 16. Translations Operation Symbols Translation Operation Symbols Translation sum of a and b product of a and b a plus b a times b b added to a a multiplied by b Addition b more than a Multiplication a increased by b the total of a and b difference of a and b quotient of a and b a minus b a divided by b b subtracted from a b divided into a Subtraction a decreased by b Division ratio of a and b b less than a a over b a less b a per b Translate each phrase to an algebraic expression. 17. x added to y 18. x subtracted from y 19. x decreased by y 20. the product of the square root of 5 and x 21. 6 less than the absolute value of p 22. three times w added to z 23. three times the sum of w and z 24. Write the English phrase as an algebraic expression. Then evaluate the expression for x = 5 and y = 2. The product of x and the square of y .

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