which of the following expressions are true?
A: 8^3x8^2<8^4
B: 4^4x4^4=4^16
C: 2^2x2^6 <2^8
A: False
8^3x8^2 can be simplified as 8^5, so the expression becomes 8^5<8^4 which is false.
B: True
When we multiply two exponential expressions with the same base, we add the exponents. So, 4^4x4^4 is equal to 4^(4+4) which is equal to 4^8. And, 4^16 is equal to 4^8x4^8. Therefore, 4^4x4^4=4^16.
C: True
2^2x2^6 is equal to 2^(2+6) which is equal to 2^8. So the expression becomes 2^8<2^8 which is also true.
Let's evaluate each expression step by step to see if they are true or false:
A: 8^3 * 8^2 < 8^4
To simplify this expression, we can use the exponent property that states a^m * a^n = a^(m + n).
Thus, 8^3 * 8^2 = 8^(3 + 2) = 8^5.
So the expression becomes: 8^5 < 8^4.
Since the base (8) is the same, we can compare the exponents.
5 is greater than 4.
Therefore, 8^5 is not less than 8^4.
Hence, expression A is false.
B: 4^4 * 4^4 = 4^16
Using the same exponent property, we can simplify this expression as well.
4^4 * 4^4 = 4^(4 + 4) = 4^8.
So the expression becomes: 4^8 = 4^16.
Since the exponents are the same, the bases are also the same.
Therefore, expression B is true.
C: 2^2 * 2^6 < 2^8
Again, we can simplify this expression using the exponent property.
2^2 * 2^6 = 2^(2 + 6) = 2^8.
So the expression becomes: 2^8 < 2^8.
Since the bases and exponents are the same, the two expressions are equal.
Therefore, expression C is false.
In summary, the expressions that are true are:
B: 4^4 * 4^4 = 4^16