Which of the following expressions is true?
A. 4^3 * 4^5 <4^12
B. 5^2 *5^4 =5^8
C. 5^2 *5^3 >5^5 ***
D. 3^2 * 3^4 = 3^2
Which of the following expressions is true?
A. 8^3 *8^2 <8^4
B. 4^4 * 4^4 =4^16
C. 3^3 * 3^3 >3^5
D. 2^2 * 2^6 <2^8 ***
please check
To determine which of the given expressions is true, we need to simplify the expressions on both sides of the equation and compare them.
For the first question:
A. 4^3 * 4^5 < 4^12:
To simplify this, we can add the exponents because we have the same base (4). So, the left side becomes 4^(3+5) = 4^8. The right side is already in simplified form as 4^12. Since 4^8 is less than 4^12, this expression is false.
B. 5^2 * 5^4 = 5^8:
Again, we can add the exponents because the base is the same (5). So, the left side becomes 5^(2+4) = 5^6. The right side is already simplified as 5^8. Since 5^6 is not equal to 5^8, this expression is false.
C. 5^2 * 5^3 > 5^5:
Adding the exponents, the left side becomes 5^(2+3) = 5^5. The right side is already simplified as 5^5. Since they are equal, this expression is true.
D. 3^2 * 3^4 = 3^2:
Adding the exponents, the left side becomes 3^(2+4) = 3^6. The right side is already simplified as 3^2. Since 3^6 is not equal to 3^2, this expression is false.
Therefore, the correct answer is C.
For the second question:
A. 8^3 * 8^2 < 8^4:
Adding the exponents, the left side becomes 8^(3+2) = 8^5. The right side is already in simplified form as 8^4. Since 8^5 is greater than 8^4, this expression is true.
B. 4^4 * 4^4 = 4^16:
Adding the exponents, the left side becomes 4^(4+4) = 4^8. The right side is already simplified as 4^16. Since 4^8 is not equal to 4^16, this expression is false.
C. 3^3 * 3^3 > 3^5:
Adding the exponents, the left side becomes 3^(3+3) = 3^6. The right side is already simplified as 3^5. Since 3^6 is greater than 3^5, this expression is true.
D. 2^2 * 2^6 < 2^8:
Adding the exponents, the left side becomes 2^(2+6) = 2^8. The right side is already simplified as 2^8. Since they are equal, this expression is false.
Therefore, the correct answer is D.
1. clearly A , since 4^8 < 4^12
2. clearly C, since 3^6 > 3^5