advanced formulas Flashcards
What is the power of a number?
The power of a number is the result of multiplying that number by itself a certain number of times.
What is the base in an expression like 2^3?
The base is the number that is being multiplied, which is 2 in this case.
What is the exponent in an expression like 2^3?
The exponent indicates how many times the base is multiplied by itself, which is 3 in this case.
What is 5^0?
5^0 equals 1.
True or False: Any non-zero number raised to the power of 1 is itself.
True.
What is the result of 10^2?
The result of 10^2 is 100.
Fill in the blank: The expression 3^4 means ___ multiplied by itself 4 times.
3
What is the value of (-2)^3?
-8.
What is the product of powers rule?
The product of powers rule states that a^m * a^n = a^(m+n).
What is the power of a power rule?
The power of a power rule states that (a^m)^n = a^(m*n).
If a = 2 and b = 3, what is a^b?
2^3 = 8.
What is 4^1/2?
4^1/2 equals 2.
True or False: 7^3 is greater than 7^2.
True.
What is the value of 2^5?
The value of 2^5 is 32.
Fill in the blank: 10^(-1) is equal to ___ .
0.1.
What is the quotient of powers rule?
The quotient of powers rule states that a^m / a^n = a^(m-n).
What is 8^(1/3)?
8^(1/3) equals 2.
What is the result of 3^2 * 3^3?
The result is 3^(2+3) = 3^5 = 243.
If x = 4, what is x^3?
x^3 = 4^3 = 64.
What does it mean to raise a number to a negative exponent?
Raising a number to a negative exponent means taking the reciprocal of the base raised to the positive exponent.
What is the value of 2^(-3)?
The value of 2^(-3) is 1/8.
True or False: The expression 5^2 is equal to 25.
True.
What is 6^2 + 6^2?
6^2 + 6^2 = 36 + 36 = 72.
What is the value of 1^100?
1^100 equals 1.
Fill in the blank: The expression 2^x represents ___ where x is any real number.
an exponential function.
