Question

11.
Find the number of zeros that the cube of each of the following number ends with.
(a) 430
(b) 1002
(c) 2010 3
(d) 32006
(e) 2003000 15 (f) 80000
plz answer me plzzzzz quick ​

Answer 1

Step-by-step explanation:

The number of consecutive zeroes in the given expression n will be three.

Solution:

To find the number of consecutive zeroes we need to separate out number of 2’s and 5’s possible in the calculation. This is because, equal number of 2’s and 5’s only lead to the formation of 10. Thus,

Given that

\begin{gathered}\begin{aligned} \mathrm { n } & = 2 ^ { 3 } \times 3 ^ { 4 } \times 7 \times 15 ^ { 6 } \\\\ & = 2 ^ { 3 } \times 3 ^ { 4 } \times 7 \times ( 3 \times 5 ) ^ { 6 } \\\\ & = 2 ^ { 3 } \times 3 ^ { 4 } \times 7 \times 3 ^ { 6 } \times 5 ^ { 3 } \times 5 ^ { 3 } \\\\ & = \left( 2 ^ { 3 } \times 5 ^ { 3 } \right) \times 3 ^ { 10 } \times 5 ^ { 3 } \times 7 \\\\ & = 3 ^ { 10 } \times 5 ^ { 3 } \times 7 \times ( 10 ) ^ { 3 } \\\\ & = 3 ^ { 10 } \times 5 ^ { 3 } \times 7 \times 1000 \end{aligned}\end{gathered}

n

=2

3

×3

4

×7×15

6

=2

3

×3

4

×7×(3×5)

6

=2

3

×3

4

×7×3

6

×5

3

×5

3

=(2

3

×5

3

)×3

10

×5

3

×7

=3

10

×5

3

×7×(10)

3

=3

10

×5

3

×7×1000