625 Words3 Pages

1. While simplifying some math work, Peter wrote on his paper that x3 • x3 • x3 • x3 equaled x3+ 3 + 3 +3 . Did Peter simplify his work correctly and completely to a final answer? Would Peter’s work be the same if he were to simplify x3 + x3 + x3 + x3?
Peter started out his work correctly, but didn’t simplify his work. He should have added the exponents up to be x^12. If he were to simplify the latter, he was end up with 4x^3 because when adding variables with like exponents, the exponent stays the same while the variables themselves are added together as normal.
2. Simplify the given expression to rational exponent form and justify each step by identifying the properties of rational exponents used. All work must be shown. One*…show more content…*

One of your friends sends you an email asking you to explain how all of the following expressions have the same answer. * The cubed root of x to the third power * x^1/3 times x^1/3 times x^1/3 times x^1/3 * 1/x^-1 * The 11th root of x^5 times x^4 times x^2 Compose an email back assisting your friend and highlight the names of the properties of exponents when you use them. * When turning a radical expression to a rational exponent, the exponent on the radicand, which is three here, becomes the numerator of the exponent. The index, or root of the radical becomes the denominator. This changes the now rational exponent to x^3/3, which simplified leaves x as the final answer. * The product of powers property states that exponents with the same base, when multiplied, add their exponents together. So we add the numerators up and keep the denominator to get x^3/3, which is simply x. * When a negative exponent is in the denominator as it is here, you make it bring it upward to make a positive. One times x^1 leaves x when simplified. * Using the product of powers property, we add the exponents together to get the 11th root of x^11. By finding the 11th root of x^11 we cancel both 11s out to get simply

One of your friends sends you an email asking you to explain how all of the following expressions have the same answer. * The cubed root of x to the third power * x^1/3 times x^1/3 times x^1/3 times x^1/3 * 1/x^-1 * The 11th root of x^5 times x^4 times x^2 Compose an email back assisting your friend and highlight the names of the properties of exponents when you use them. * When turning a radical expression to a rational exponent, the exponent on the radicand, which is three here, becomes the numerator of the exponent. The index, or root of the radical becomes the denominator. This changes the now rational exponent to x^3/3, which simplified leaves x as the final answer. * The product of powers property states that exponents with the same base, when multiplied, add their exponents together. So we add the numerators up and keep the denominator to get x^3/3, which is simply x. * When a negative exponent is in the denominator as it is here, you make it bring it upward to make a positive. One times x^1 leaves x when simplified. * Using the product of powers property, we add the exponents together to get the 11th root of x^11. By finding the 11th root of x^11 we cancel both 11s out to get simply

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