Write 2 x 8 x 64 in index notation with the smallest base.

Question

Write 2 x 8 x 64 in index notation with the smallest base.

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Dâu 4 years 2021-07-25T19:57:55+00:00 2 Answers 21 views 0

Answers ( )

  1. thugiang
    0
    2021-07-25T19:59:17+00:00
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    Answer:

    Step-by-step explanation:

    Prime factorize 8 and 64

    8 = 2* 2 * 2 = 2³

    64 = 2*2*2 *2*2*2 = 2⁶

    2*8*64 = 2* 2³ *2⁶ = 2¹⁺³⁺⁶ = 2¹⁰

    In exponent multiplication, if base are same, then add the exponents.

  2. Nho
    0
    2021-07-25T19:59:22+00:00
    Reply

    \sf{\bold{\blue{\underline{\underline{Given}}}}}

    • 2
    • 8
    • 64⠀⠀⠀⠀

    \sf{\bold{\red{\underline{\underline{To\:Find}}}}}

    • ⠀Write 2 x 8 x 64 in index notation with the smallest base.⠀⠀⠀

    \sf{\bold{\purple{\underline{\underline{Solution}}}}}

    The prime factors of

    • 2=2×1
    • 8=2×2×2×1
    • 64=2×2×2×2×2×2×1

    Sooo,

    • ⠀⠀\sf{2=2^{1} }
    • \sf{8=2^{3} }
    • \sf{64=2^{6} }

    According to the question

    • 2×8×64
    • \sf{2^{1}×2^{3}×2^{6} }
    • \sf{2^{1+3+6} }
    • \sf{ 2^{10} }

    \sf{\bold{\green{\underline{\underline{Answer}}}}}

    ⠀⠀⠀⠀

    2 x 8 x 64 in index notation with the smallest base is \sf{2^{10} }

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