Powers
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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| Product of Powers Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, b^m x b^n = b^m+n
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| Power of a Power Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, (b^m)^n = b^m x n
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| Power of a Product Postulate | For any nonnegative bases and nonzero real exponents, or any nonzero bases and integer exponents, (ab)^m = a^m b^m
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| Quotient of Powers Postulate | (b^m)/(b^n) = b^m-n
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| Power of a Quotient Postulate | (a/b)^m = (a^m)/(b^m)
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| Zero Exponent Theorem | if b is a nonzero real number, b^0 = 1
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| Negative Exponent Theorem | For any positive base b and real exponent n, or any nonzero base b and integer exponent n, b^-n = 1/(b^n)
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| Annual Compound Interest Formula | A = P(1 + r)^t when P is the amount of money invested at an annual interest rate of r compounded annually. Let A be the total amount after t years.
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| General Compound Interest Formula | Let P be the amount invested at an annual interest rate r compounded n times per year. Let A be the amount after t years. Then
A = P(1 + (r/n))^nt
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| Explicit Formula for a Geometric Sequence | In the geometric sequence with first term g*q and constant ratio r, g*n = g*1(r)^n-1
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| Number of Real Roots Theorem | Every positive real number has: 2 real nth roots, when n is even. 1 real nth root, when n is odd.
Every negative real number has: 0 real nth roots, when n is even.
1 real nth root when n is odd.
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Created by:
katelesperance
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