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Math Help - Exponents numbers

  1. #1
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    Exponents numbers

    if 2^5 = 32 then 2^100 is close to

    a 10^10 b 10^15 c 10^10 d 10^25 e 10^30
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  2. #2
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    Hello, sri340!

    If  2^5 = 32, then  2^{100} is close to:

    (a)\;10^{10} \qquad(b)\;10^{15} \qquad(c)\;10^{10} \qquad(d)\;10^{25} \qquad(e)\;10^{30}

    Given: . 2^5 \:=\:32

    Square: . \left(2^5\right)^2 \:=\:32^2 \quad\Rightarrow\quad 2^{10} \:=\:1024

    . . . . . . . 2^{10} \;\approx\;1000 \quad\Rightarrow\quad 2^{10} \;\approx\;10^3


    Raise to the 10th power: . \left(2^{10}\right)^{10} \:\approx\:\left(10^3\right)^{10}

    Therefore: . 2^{100} \;\approx\;10^{30} . . . answer (e)

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