The Power of Exponents
What is the value of 2^3?
- 2^3 means 2 multiplied by itself three times. Therefore, 2^3 = 2 x 2 x 2 = 8.
What is the simplified form of (3^2)^3?
- (3^2)^3 means 3^2 multiplied by itself three times. Therefore, (3^2)^3 = 3^6 = 729.
What is the value of 5^-2?
- 5^-2 means 1 divided by 5 squareTherefore, 5^-2 = 1/5^2 = 1/25 = 0.04.
What is the product of 10^3 and 10^4?
- When multiplying powers with the same base, you add the exponents. Therefore, 10^3 x 10^4 = 10^(3+4) = 10^7.
What is the value of (-2)^4?
- (-2)^4 means -2 multiplied by itself four times. Since an even number of negative factors always result in a positive value, (-2)^4 = 2^4 = 16.
What is the simplified form of 4^3/4^2?
- When dividing powers with the same base, you subtract the exponents. Therefore, 4^3/4^2 = 4^(3-2) = 4^1 = 4.
What is the value of 2^0?
- Any number raised to the power of 0 is equal to 1; therefore, 2^0 = 1.
What is the simplified form of (2^2 x 3^3)^2/2^4?
- When raising a power to another power, you multiply the exponents. When dividing powers with the same base, you subtract the exponents. Therefore, (2^2 x 3^3)^2/2^4 = (2^4 x 3^6)/2^4 = 3^6 = 729.
What is the value of (-3)^3 x (-3)^2?
- When multiplying powers with the same base, you add the exponents. Therefore, (-3)^3 x (-3)^2 = (-3)^(3+2) = (-3)^5 = -243.
What is the value of 10^-3 x 5^3?
- When multiplying powers with different bases, you cannot simplify them further. Therefore, 10^-3 x 5^3 = 10^-3 x 125 = 0.125.
