Which of the following expressions is true?
A: 4^3x4^5<4^12
B: 5^2x5^3>5^5
C: 3^2x3^4=3^2
D: 5^2x5^4=5^8
D: 5^2x5^4=5^8
When multiplying exponential expressions with the same base, you add the exponents. Therefore:
A: 4^3x4^5 = 4^(3+5) = 4^8 which is NOT less than 4^12.
B: 5^2x5^3 = 5^(2+3) = 5^5 which is NOT greater than 5^5.
C: 3^2x3^4 = 3^(2+4) = 3^6 which is NOT equal to 3^2.
D: 5^2x5^4 = 5^(2+4) = 5^8, which IS equal to 5^8.
To determine which expression is true, let's simplify each expression step by step:
A: 4^3 x 4^5 < 4^12
We can simplify both sides of the inequality by adding the exponents:
4^(3+5) < 4^12
4^8 < 4^12
B: 5^2 x 5^3 > 5^5
Again, we can simplify both sides of the inequality by adding the exponents:
5^(2+3) > 5^5
5^5 > 5^5
C: 3^2 x 3^4 = 3^2
When multiplying two exponents with the same base, we add the exponents:
3^(2+4) = 3^2
3^6 = 3^2
Since 3^6 is not equal to 3^2, this expression is not true.
D: 5^2 x 5^4 = 5^8
Again, adding the exponents on both sides of the equation:
5^(2+4) = 5^8
5^6 = 5^8
Since 5^6 is not equal to 5^8, this expression is not true.
So, the only true expression among the given choices is A: 4^3 x 4^5 < 4^12.