Establishing
Write true if the statement is true and false if it is
false.
1. If N is a positive real number, then 0^N = 0
2. For any real number x, x^0 = 1.
3. The expression 3^4 is read "three raised to the
fourth power".
4.If p is a nonzero real number and N is a positive integer, then p^n and p^-N are reciprocals.
5. If b is a real number, b^3. b^4 = b^12
1. True
2. True
3. True
4. False
5. False
1. True. When any real number (including zero) is raised to the power of zero, the result is always 1. So, 0^N = 0 is false.
2. False. When any real number (except zero) is raised to the power of zero, the result is always 1. So, x^0 = 1 is true.
3. True. The expression 3^4 is read as "three raised to the fourth power".
4. False. If p is a nonzero real number and N is a positive integer, then p^n and p^-N are not reciprocals.
5. False. When multiplying two numbers with the same base and different exponents, you add the exponents. So, b^3 * b^4 = b^(3+4) = b^7, not b^12.