Exploring Laws of Exponents on Real Numbers

Question 1:
Simplify the expression 5^2 × 5^3.
A) 25^5
B) 5^6
C) 5^5
D) 10^5

Answer: B) 5^6
Explanation: When multiplying numbers with the same base, we add the exponents. In this case, 5^2 × 5^3 = 5^(2+3) = 5^5 = 5^6.

Question 2:
What is the value of (3^4)^2?
A) 9^8
B) 3^8
C) 3^6
D) 81^2

Answer: A) 9^8
Explanation: When raising a power to another power, we multiply the exponents. Therefore, (3^4)^2 = 3^(4*2) = 3^8 = 9^4 = 9^8.

Question 3:
Simplify the expression (2^3)^4 ÷ 2^2.
A) 2^6
B) 2^10
C) 2^11
D) 2^12

Answer: C) 2^11
Explanation: First simplify the numerator: (2^3)^4 = 2^(3*4) = 2^12. Then divide by 2^2 to get 2^12 ÷ 2^2 = 2^(12-2) = 2^10 = 2^11.

Question 4:
If 6^x = 216, what is the value of x?
A) 2
B) 3
C) 4
D) 5

Answer: B) 3
Explanation: 216 can be expressed as 6^3, so x = 3.

Question 5:
What is the result of (4^2) × (4^(-3))?
A) 1/64
B) 1/16
C) 256
D) 16

Answer: A) 1/64
Explanation: When multiplying with negative exponents, we subtract the exponents. Therefore, (4^2) × (4^(-3)) = 4^(2-3) = 4^(-1) = 1/4 = 1/64.