Rules / formulas Flashcards
What is the product of powers rule for exponents?
When multiplying two powers with the same base, add the exponents.
If a^m * a^n = a^?
a^(m+n)
True or False: The power of a product rule states that (ab)^n = a^n * b^n.
True
Fill in the blank: The power of a power rule states that (a^m)^n = a^__.
mn
What is the formula for the power of a quotient?
If a ≠ 0, then (a/b)^n = a^n / b^n.
If (x^3)^2 = x^?
6
What is the zero exponent rule?
Any non-zero base raised to the zero power equals one.
What is the value of 5^0?
1
True or False: a^(-n) = 1/a^n.
True
If a^3 = 27, what is the value of a?
3
What does the expression a^(1/n) represent?
The n-th root of a.
If a = 2 and b = 3, what is (ab)^2?
36
What is the formula for the difference of squares involving exponents?
a^2 - b^2 = (a-b)(a+b)
If 4^x = 64, what is the value of x?
3
Fill in the blank: The expression a^(m/n) is equivalent to the __.
n-th root of a raised to the m-th power.
What is the formula for the sum of cubes?
a^3 + b^3 = (a+b)(a^2 - ab + b^2)
True or False: The expression a^m / a^n can be simplified to a^(m+n).
False
If x^2 * x^5 = x^?
7
What is the value of (3^2)^3?
729
If 2^x = 16, what is x?
4
Fill in the blank: The expression (a/b)^-n is equivalent to __.
b^n / a^n
If a = 5 and b = 2, what is a^3 * b^2?
125 * 4 = 500
What is the rule for raising a product to a power?
The power of a product rule.
What is the value of 10^(-1)?
0.1
If (x^2y^3)^2 = x^?y^?
4, 6
