Which of the following expressions is true?
A) 5^2∙5^3=5^6
B) 4^2∙4^3<4^5
C) 3^6∙3^4>3^9
D)2^3∙2^4=4^7
A) 5^2∙5^3=5^6 is true since when multiplying powers with the same base, you add their exponents. So 5^2∙5^3 = 5^(2+3) = 5^5, which is equivalent to 5^6/5.
To determine which expression is true, we need to simplify each expression and compare the results.
Let's simplify each expression step-by-step:
A) 5^2 * 5^3 = 5^6
To simplify, we add the exponents when we multiply powers with the same base:
5^2 * 5^3 = 5^(2+3) = 5^5.
So, A) 5^2 * 5^3 is NOT equal to 5^6.
B) 4^2 * 4^3 < 4^5
Following the same logic, simplify each expression:
4^2 * 4^3 = 4^(2+3) = 4^5.
Therefore, B) 4^2 * 4^3 is equal to 4^5.
C) 3^6 * 3^4 > 3^9
Apply the same process:
3^6 * 3^4 = 3^(6+4) = 3^10.
Thus, C) 3^6 * 3^4 is NOT greater than 3^9.
D) 2^3 * 2^4 = 4^7
Again using the simplification rule:
2^3 * 2^4 = 2^(3+4) = 2^7.
But 2^7 is not equal to 4^7. Therefore, D) 2^3 * 2^4 is NOT equal to 4^7.
So, the only true expression among the options is B) 4^2 * 4^3 < 4^5.