AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 3 Medium

How many digits are in the base-ten representation of {{25}^{16}}\times {{2}^{38}}?

  • A.

    30

  • B.

    32

  • C.

    34

  • D.

    36

  • E.

    38

Answer:C

{{25}^{16}}\times {{2}^{38}}={{25}^{16}}\times {{4}^{19}}=(2{{5}^{16}}\times {{4}^{16}})\times {{4}^{3}}={{(25\times 4)}^{16}}\times 64=64\times {{100}^{16}}=64\times {{10}^{32}}.

Thus, {{25}^{16}}\times {{2}^{38}} has 34 digits.

Choose \boxed{\text{B}}.

Related Problems
Problem 1 AMC 10 Daily Practice Round 1
Problem 2 AMC 10 Daily Practice Round 1
Problem 4 AMC 10 Daily Practice Round 1
Problem 5 AMC 10 Daily Practice Round 1
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