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  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
    $\displaystyle 28 = 2.8 \times 10$

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


    For your second question it's an arithmetic error on the exponent $\displaystyle -3-6 = -9$ whereas you have -8
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  3. #3
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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: $\displaystyle a^x \cdot a^y=a^{x+y}$

    Your problem:

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

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

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

    $\displaystyle 20 \times 10^{-9}=$

    $\displaystyle 2.0 \times 10^{-8}$

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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.

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

    Hence

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

    You made an error in the second one.

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

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