SOLUTION: how many digits are in the number represented by the expression 2 to the power of 5201 times 5 to the power of 2560 divided by 8 to the power of 882??? please help me I've bee

Algebra ->  Exponents -> SOLUTION: how many digits are in the number represented by the expression 2 to the power of 5201 times 5 to the power of 2560 divided by 8 to the power of 882??? please help me I've bee      Log On


   

Question 1070032: how many digits are in the number represented by the
expression 2 to the power of 5201 times 5 to the power of
2560 divided by 8 to the power of 882???
please help me I've been stuck on this question for 1 hour now
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
how many digits are in the number represented by the
expression 2 to the power of 5201 times 5 to the power of
2560 divided by 8 to the power of 882???
%282%5E5201%2A5%5E2560%29%2F8%5E882%22%22=%22%22

%282%5E%282641%2B2560%29%2A5%5E2560%29%2F%282%5E3%29%5E882%22%22=%22%22

%282%5E2641%2A2%5E2560%2A5%5E2560%29%2F2%5E2646%22%22=%22%22

%282%5E2641%2A%282%5E2560%2A5%5E2560%29%29%2F2%5E2646%22%22=%22%22

%282%5E2641%2A10%5E2560%29%2F2%5E2646%22%22=%22%22

%2810%5E2560%29%2F2%5E5%22%22=%22%22

%2810%5E2560%29%2F32%22%22=%22%22

expr%281%2F32%29%2A%2810%5E2560%29%22%22=%22%22

0.03125%2A%2810%5E2560%29%22%22=%22%22

3.125%2A10%5E%28-2%29%2A%2810%5E2560%29%22%22=%22%22

3.125%2A10%5E2558%22%22=%22%22

So since 10%5E1=10 has 2 digits and
10%5E2=100 has 3 digits, etc.,
then 10%5E2558 has 2559 digits, and
so does 3.125%2A10%5E2558

Edwin