which expression is true?
A: 8^3x8^2<8^4
B: 4^4x4^4=4^16
C: 2^2x2^6 <2^8
D: 3^3x3^3>3^5
B: 4^4x4^4=4^16
Let's evaluate each expression step by step to determine which one is true.
A: 8^3x8^2 < 8^4
To solve this, we can simplify the exponents:
8^3 = 8 x 8 x 8 = 512
8^2 = 8 x 8 = 64
8^4 = 8 x 8 x 8 x 8 = 4096
Now let's substitute the simplified values into the expression:
512 x 64 < 4096
32768 < 4096
This statement is false, so A is not true.
B: 4^4x4^4 = 4^16
To solve this, we can simplify the exponents:
4^4 = 4 x 4 x 4 x 4 = 256
4^16 = 4 x 4 x 4 x ... x 4 (16 times)
Now let's substitute the simplified values into the expression:
256 x 256 = 65536
This statement is true, so B is true.
C: 2^2x2^6 < 2^8
To solve this, we can simplify the exponents:
2^2 = 2 x 2 = 4
2^6 = 2 x 2 x 2 x 2 x 2 x 2 = 64
2^8 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256
Now let's substitute the simplified values into the expression:
4 x 64 < 256
256 < 256
This statement is false, so C is not true.
D: 3^3x3^3 > 3^5
To solve this, we can simplify the exponents:
3^3 = 3 x 3 x 3 = 27
3^5 = 3 x 3 x 3 x 3 x 3 = 243
Now let's substitute the simplified values into the expression:
27 x 27 > 243
729 > 243
This statement is true, so D is true.
Therefore, the correct answer is B: 4^4x4^4 = 4^16.