That number becomes an exponent. For example, 5 to the -2 power is 1/25
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Anything to the power of a negative number is equal to one divided that "anything" raised to the positive value of the exponent. For example:a-b = 1/ abSo you can think of this by expressing the number as a fraction. Consider, what is 0.1 as a fraction? The answer is 1/10. This means that when expressed as an exponent, it would be 10-1.
The direction of the inequality remains unchanged. The direction changes when you divide or multiply both sides by a negative number. It also changes if both sides are raised to a negative exponent.
If your calculator is advanced, like the TI-84, there is an exponent button you can hit. Then, just Type negative and the exponent. If it is a simpler calculator, like a four-function calculator, there IS a way. By raising a number to a negative exponent, you are saying that one is being divided by that number to the positive version of that power. Ex: 5^-8 = 1/(5^8). To do this, divide one by the base, then raise it to the exponent, making sure that the exponent is POSITIVE. Also be careful that the entire denominator is in parentheses, just in case.
Example: (4x)-2 The answer to this would be 1/ 16x2. Multiply it out as if the negative exponent was not there ((4x)2), then that will be the denominator of the fraction. The numerator is one.
negative 8 would be the base and the 15 would be the exponent