Question

How many factors of 4^8*6^3*7^2 are perfect squares?

Answer 1

Answer:

20

Step-by-step explanation:

For perfect square, the power of each should be even.

Factor of 4^8 (that are perfect square)= 4^0, 4^2, 4^4, 4^6, 4^8;

So, the number of factors are 5.

Factor of 6^3 (that are perfect square) = 6^0, 6^2;  

therefore, the Number of factors that are perfect squares for 6^3 is 2

Factor of 7^2 (that are perfect square) = 7^0, 7^2;  

Number of factors that are perfect squares for 7^2 is also 2

Any combination of the above factors will result in a perfect square when multiplied together.

hence, Total No. of combination = 5*2*2 =20

Thus, 20 factors of 4^8*6^3*7^2 are perfect squares.

Answer 2

Answer:

39

Step-by-step explanation:

4⁸ × 6³ × 7²

4 = 2²  

= (2²)⁸ × 6³ × 7²

= (2²)⁸ × 6² × 7²  × 6

6 = 2 × 3

= (2²)⁸ × 2² × 3² × 7²  × 6

= (2²)⁹ × 3² × 7²  × 6

9 time 2²

1 time 3²

1 time 7²

total factors of combination

39