I need help on zero and negative exponents
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Sure, I can help you with zero and negative exponents. What specifically would you like to know or understand about these topics?
Sure, I can help you with zero and negative exponents!
Let's start with zero exponents. Any number (except for zero itself) raised to the power of zero is always equal to 1. It doesn't matter if the base is positive or negative, the result is still 1.
For example:
- 5^0 = 1
- (-2)^0 = 1
- 10^0 = 1
To understand why this is true, you can think of any number raised to a power as repeated multiplication. When you raise a number to the power of zero, there are no multiplications happening, so the result is 1.
Now, let's move on to negative exponents. A negative exponent indicates that we need to apply the reciprocal of the number raised to the positive exponent. In other words, we flip the base and make the exponent positive.
For example:
- 2^-3 = 1 / (2^3)
- (1/4)^-2 = 1 / ((1/4)^2)
- (-3)^-4 = 1 / ((-3)^4)
To calculate these values, we can follow these steps:
1. Rewrite the expression with a positive exponent by taking the reciprocal of the base.
2. Evaluate the positive exponent.
3. Simplify the expression if necessary.
For instance:
- 2^-3 = 1 / (2^3) = 1 / 8 = 1/8
- (1/4)^-2 = 1 / ((1/4)^2) = 1 / (1/16) = 16
- (-3)^-4 = 1 / ((-3)^4) = 1 / 81 = 1/81
I hope this explanation helps you understand zero and negative exponents better. Let me know if you have any further questions!