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Math Help - exponentials

  1. #1
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    exponentials

    Without a calculator how would I calculate multiplication exponential expression

    The formula is a^x a^ y = a ^x+ y

    (7 x 10^ 2) x (4 x 10 ^ 5)
    i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
    so what am I doing wrong?

    in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
    i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

    Thank you
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  2. #2
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    Quote Originally Posted by batki610 View Post
    Without a calculator how would I calculate multiplication exponential expression

    The formula is a^x a^ y = a ^x+ y

    (7 x 10^ 2) x (4 x 10 ^ 5)
    i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
    so what am I doing wrong?

    in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
    i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

    Thank you
    28 = 2.8 \times 10

    They are the same answer but your book is using scientific notation which is of the form  a \times 10^n  \text{  where  } 1 < a \leq 10 \text{  and  } n \in \mathbb{Z}
    (if you don't understand what \mathbb{Z} is - it means the integers)


    For your second question it's an arithmetic error on the exponent -3-6 = -9 whereas you have -8
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  3. #3
    A riddle wrapped in an enigma
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    Quote Originally Posted by batki610 View Post
    Without a calculator how would I calculate multiplication exponential expression

    The formula is a^x a^ y = a ^x+ y

    (7 x 10^ 2) x (4 x 10 ^ 5)
    i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
    so what am I doing wrong?

    in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
    i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

    Thank you

    Hi batki610,

    Your rule is correct: a^x \cdot a^y=a^{x+y}

    Your problem:

    (5 \times 10^{-3}) \times (4 \times 10^{-6})=

    (5 \times 4) \times (10^{-3} \times 10^{-6})=

    20 \times 10^{-3+(-6)}=

    20 \times 10^{-9}=

    2.0 \times 10^{-8}

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  4. #4
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    Quote Originally Posted by batki610 View Post
    Without a calculator how would I calculate multiplication exponential expression

    The formula is a^x a^ y = a ^(x+ y)

    (7 x 10^ 2) x (4 x 10 ^ 5)
    i thought the answer would be 28 x 10^ 7 but the answer key has 2.8 x 10 ^ 8
    so what am I doing wrong?

    in the similar way, (5 x 10 ^ -3) x ( 4 x 10^ -6)
    i thought the answer would be 20 x 10 ^ -8 but the answer is 2 x 10 ^-8

    Thank you
    Your answer key is expecting an answer written as a value between 1 and 10 times a power of 10.

    28=(2.8)(10)=2.8\times 10^1

    Hence

    28\times 10^7=2.8\times 10^1\times 10^7=2.8\times 10^{1+7}

    You made an error in the second one.

    10^{-3}\times 10^{-6}=10^{-3-6}

    Finally, express the answer as 2\times 10^y
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