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Math Help - simplify and express using exponents

  1. #1
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    simplify and express using exponents

    i dont normally ask help in math but plzzz help me its urgent i dont know what to do its like a times a times a examples: notes The Algebra Tutor

    Lesson #5
    Exponents & Properties of Exponents

    Learn about powers, exponential notation, comparison of numbers versus quantities to squares and cubes. Numbers with exponents of one and zero are also covered.


    QUESTIONS FOR THOUGHT AND FURTHER STUDY
    1. Why do we use exponents?
    2. What is exponential notation?
    3. Compare 3(X2) and 3X2.
    4. Any non zero number (X) to the
    zero power equals?
    5. Why is it important to follow the
    order of operation?

    ANSWERS
    1. It is a shorter and condensed way of writing products.
    2. A term for a power using exponents.
    3 Following the order of operations, the X2 IN 3(X2) is performed first and in 3X2, 3 times X is performed first and then that number is squared.
    4. 1
    5. The solution to the problem will not be correct if the problem is not solved with the proper order of operations.


    STUDENT VOCABULARY
    Exponent: A number that indicates the operation of repeated multiplication.

    Power: The number that represents the operation of repeated multiplication.
    Example: The third power of 4 equals 43 equals 4 times 4 times 4.

    Exponential Notation: An expression of a power using exponents.

    Expression: A term used for a mathematical symboI.

    Order of Operations: The proper sequence used to solve expressions.
    Example: In the equation 2(X+3) the first operation is to perform the X+3 then multipIy by 2.

    Positive Exponents: Exponents with values greater than 0.

    Negative Exponents: Exponents with values less than 0.


    PRACTICE PROBLEMS
    I. 5 times 5 in exponential notation.

    2. Write A times A times A times A in exponential notation.

    3. Evaluate 8 to the third power or 8 cubed.

    4. Evalute 1.2 to the second power, or 1.2 squared.

    5. Evaluate X to the fifth power, when X equals 3.

    6. Evalute 4 times X squared and 4X quantity squared, when X equals 3.

    7. Evaluate A equal pi times R squared when R equals 4. Use 3.14 for pi.

    8. Evaluate 3A quantity cubed when A equals negative 3.

    9. Evaluate negative 5 to the first power and to the zero power.

    10. Evaluate 0 to the first power and to the zero power.
    11. Express 5 to the negative 2 power with positive exponents and then simplify.

    12. Express 3 times X to the negative 4 power with positive exponents.

    13. Express 1 over 2Y quantity to the negative 3 power with positive exponents.

    14. Express T to the seventh power with negative exponents.

    ANSWERS:
    1. 52
    2. A4
    3. 512
    4. 1.44
    5. 243
    6. 36, 144 Expressions not equal
    7. 50.24
    8. -729
    9. -5, 1
    10. 0 Undefined
    11. 1/25
    12. 3/X4
    13. 2Y3
    14. 1/T-7

    can u plz teach me in a way a dummy can understand like play by play details thx in advance
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by NozZ View Post
    i dont normally ask help in math but plzzz help me its urgent i dont know what to do its like a times a times a examples: notes The Algebra Tutor

    Lesson #5
    Exponents & Properties of Exponents

    Learn about powers, exponential notation, comparison of numbers versus quantities to squares and cubes. Numbers with exponents of one and zero are also covered.


    QUESTIONS FOR THOUGHT AND FURTHER STUDY
    1. Why do we use exponents?
    2. What is exponential notation?
    3. Compare 3(X2) and 3X2.
    4. Any non zero number (X) to the
    zero power equals?
    5. Why is it important to follow the
    order of operation?

    ANSWERS
    1. It is a shorter and condensed way of writing products.
    2. A term for a power using exponents.
    3 Following the order of operations, the X2 IN 3(X2) is performed first and in 3X2, 3 times X is performed first and then that number is squared.
    4. 1
    5. The solution to the problem will not be correct if the problem is not solved with the proper order of operations.


    STUDENT VOCABULARY
    Exponent: A number that indicates the operation of repeated multiplication.

    Power: The number that represents the operation of repeated multiplication.
    Example: The third power of 4 equals 43 equals 4 times 4 times 4.

    Exponential Notation: An expression of a power using exponents.

    Expression: A term used for a mathematical symboI.

    Order of Operations: The proper sequence used to solve expressions.
    Example: In the equation 2(X+3) the first operation is to perform the X+3 then multipIy by 2.

    Positive Exponents: Exponents with values greater than 0.

    Negative Exponents: Exponents with values less than 0.


    PRACTICE PROBLEMS
    I. 5 times 5 in exponential notation.

    2. Write A times A times A times A in exponential notation.

    3. Evaluate 8 to the third power or 8 cubed.

    4. Evalute 1.2 to the second power, or 1.2 squared.

    5. Evaluate X to the fifth power, when X equals 3.

    6. Evalute 4 times X squared and 4X quantity squared, when X equals 3.

    7. Evaluate A equal pi times R squared when R equals 4. Use 3.14 for pi.

    8. Evaluate 3A quantity cubed when A equals negative 3.

    9. Evaluate negative 5 to the first power and to the zero power.

    10. Evaluate 0 to the first power and to the zero power.
    11. Express 5 to the negative 2 power with positive exponents and then simplify.

    12. Express 3 times X to the negative 4 power with positive exponents.

    13. Express 1 over 2Y quantity to the negative 3 power with positive exponents.

    14. Express T to the seventh power with negative exponents.

    ANSWERS:
    1. 52
    2. A4
    3. 512
    4. 1.44
    5. 243
    6. 36, 144 Expressions not equal
    7. 50.24
    8. -729
    9. -5, 1
    10. 0 Undefined
    11. 1/25
    12. 3/X4
    13. 2Y3
    14. 1/T-7

    can u plz teach me in a way a dummy can understand like play by play details thx in advance
    you put a lot of stuff down here. perhaps you could be a bit more specific with what's bugging you?
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  3. #3
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    will today am been having a lot on my mind and am better with the teacher and i was wondering if someone can put this vocabulary and ways i can understand better and today i had a sub so yeah by the way those aren't "my notes" so am completely clumsy so please help me step by step
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  4. #4
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    Quote Originally Posted by NozZ View Post
    i dont normally ask help in math but
    I must ask you why that is?
    It seems to me that you have a great many issues with very basic mathematics.
    The fact is that anyone who is mathematical challenged, is doomed to failure is this modern world.
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    ok, so you need help with vocabulary, huh? let's get to it.

    Quote Originally Posted by NozZ View Post
    STUDENT VOCABULARY
    Exponent: A number that indicates the operation of repeated multiplication.
    baby talk: exponents are those little numbers or variables or expressions to the top right of some other number or variable or expression. when this number is a positive integer, it describes how many times the base is being multiplied.

    example: 5^4

    here, 4 is the exponent, 5 is the base. this tells us that we have 4 5's being multiplied together, that is, 5^4 = 5 \times 5 \times 5 \times 5

    when the exponent is rational, it describes something else, see post #3 here

    Power: The number that represents the operation of repeated multiplication.
    Example: The third power of 4 equals 43 equals 4 times 4 times 4.
    another name for exponent. well, used in a different context. since we are talking about vocabulary, we can say, "exponent" is kind of a noun, while "power" can be a noun or an adjective, or whatever

    Exponential Notation: An expression of a power using exponents.
    this is writing a number as a base raised to some power or exponent.

    example, writing 5^4 instead of 5 \times 5 \times 5 \times 5 or 625

    Expression: A term used for a mathematical symboI.
    this is more accurately described as a mathematical phrase or "term", pardon the pun.

    any meaningful combination of numbers and/or variables can be called an expression.

    2x + 3 is an expression, so is 3x^2 + 5

    we say something like y = 2x + 4 is "expressing y in terms of x"

    Order of Operations: The proper sequence used to solve expressions.
    Example: In the equation 2(X+3) the first operation is to perform the X+3 then multipIy by 2.
    this is just saying what order you should do what operation. there are many mnemonics for this. PEMDAS, BOMDAS, BODMAS, etc. are you familiar with these?

    [quote]
    Positive Exponents: Exponents with values greater than 0.

    Negative Exponents: Exponents with values less than 0.
    [/quotes]self explanatory.

    something to note about negative exponents though. THEY DO NOT CHANGE THE SIGN OF THE BASE. they simply mean to take the inverse. that is,

    5^{-2} = \frac 1{5^2} = \frac 1{25}

    or x^{-1/2} = \frac 1{x^{1/2}} = \frac 1{\sqrt{x}}
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  6. #6
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    thx i guess all the needed was more knowledge of the vocabulary :
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