Question

Find the number of digits in the product of 5^72 X 8^27

Answer 1

Answer:

The number of digits in the product of 5^72*8^27 are 75

Step-by-step explanation:

$5^{72}\times8^{27}$

$=5^{72}\times(2^3)^{27}$

$=5^{72}\times2^{81}$            (∵ $(a^m)^n = a^{mn}$)

$=5^{72}\times2^{72+9}$

$=5^{72}\times2^{72}\times2^9$          (∵ $a^{m} \times a^{n}=a^{m+n}$)

$=(5\times2)^{72}\times2^{9}$              (∵ $a^m \times b^m=(ab)^m$)

$=(10)^{72}\times2^{9}$

$=512\times10^{72}$

This means there will be 72 zeroes after 512!

Therefore, the number of digits in the product will be 72+3 = 75

Hope this helps.

Answer 2

Answer:

The number of digits in the product is 75.

Step-by-step explanation:

Given : Expression $5^{72}\times 8^{27}$

To find : The number of digits in the product ?

Solution :

Step 1 - Write the expression,

$5^{72}\times 8^{27}$

$5^{72}\times(2^3)^{27}$

Step 2 - Applying power rule, $(a^m)^n = a^{mn}$

$5^{72}\times2^{81}$

Step 3 - Split the power,

$5^{72}\times2^{72+9}$

$5^{72}\times2^{72}\times2^9$

Step 4 - Multiplying when power is same, $a^m \times b^m=(ab)^m$

$(5\times2)^{72}\times2^{9}$

$(10)^{72}\times2^{9}$

$512\times10^{72}$

Number of digits are 3+72=75

Therefore, The number of digits in the product is 75.