Which of the following expressions is true?
A) 2^4 x 2^3=2^12
B) 3^3 x 3^6>3^8
C) 4^2 x 4^2 4^4
D) 5^5 x 5^2 = 5^10
D) 5^5 x 5^2 = 5^10
To determine which of the following expressions is true, let's evaluate each one step-by-step:
A) 2^4 x 2^3 = 2^(4+3) = 2^7 = 128
B) 3^3 x 3^6 = 3^(3+6) = 3^9
To determine if 3^9 is greater than 3^8, we can simplify:
3^9 = 19,683
3^8 = 6,561
Since 19,683 is greater than 6,561, the expression 3^3 x 3^6 > 3^8 is true.
C) 4^2 x 4^2 4^4 = 4^(2+2+4) = 4^8
D) 5^5 x 5^2 = 5^(5+2) = 5^7
To determine if 5^7 is equal to 5^10, we can simplify:
5^7 = 78,125
5^10 = 9,765,625
Since 78,125 is not equal to 9,765,625, the expression 5^5 x 5^2 = 5^10 is false.
Therefore, the true expression is:
B) 3^3 x 3^6 > 3^8