#1**+4 **

How many even perfect square factors does 2^4*7^9 have?

**From the considerations below I can see the answer is 10**

\(7^2, \qquad 7^4, \qquad 7^6,\qquad 7^8 \qquad \text{none of these are even } \\~\\ \\ \text{all those below are even}\\ 2^2, \qquad 2^2*7^2, \qquad 2^2*7^4, \qquad 2^2*7^6,\qquad 2^2*7^8 \\ 2^4, \qquad 2^4*7^2, \qquad 2^4*7^4, \qquad 2^4*7^6,\qquad 2^4*7^8 \\ \)

Melody
Apr 28, 2018

#1**+4 **

Best Answer

How many even perfect square factors does 2^4*7^9 have?

**From the considerations below I can see the answer is 10**

\(7^2, \qquad 7^4, \qquad 7^6,\qquad 7^8 \qquad \text{none of these are even } \\~\\ \\ \text{all those below are even}\\ 2^2, \qquad 2^2*7^2, \qquad 2^2*7^4, \qquad 2^2*7^6,\qquad 2^2*7^8 \\ 2^4, \qquad 2^4*7^2, \qquad 2^4*7^4, \qquad 2^4*7^6,\qquad 2^4*7^8 \\ \)

Melody
Apr 28, 2018