a number raised to a negative exponent is a negative
If you raise 2 to the -3 power, it will be 1/8. e.g. Raising a nonzero number to the −1 power produces its reciprocal. Thus: Raising 0 to a negative power would imply division by 0, and so is undefined. A negative integer exponent can also be seen as repeated division by the base. Exponents are also known as powers of numbers. Exponents are written as. where a is referred to as the base and n is known as the exponent, and the whole expression is said to be: a raised to the power of n. is the same as saying: multiply a by itself n times. Positive Exponents. Positive Exponents or powers have the effect of multiplying the base by itself as many times as the value of the exponent. As a general form, we say that if n is positive, then. is the same as multiplying a by a, n times. The above is also true if the exponent is a negative whole number: You can try out different negative numbers and raise them to even whole numbers and the result is always a positive number. Conversely, when a negative base is raised to an odd whole number exponent, the result is ALWAYS a negative number. As a general rule, any variable or non-zero number raised to the power zero is equal to one. This is always true regardless of what the base a is. The base can be a non-zero number or a variable, positive or negative and, as long as it is raised to the power zero, it will equal to one. Report Abuse. Raising a number to a negative power does not necessarily mean it is negative. The negative means that you are raising the reciprocal to that power. In other words 2 raised to the negative 2 power is the same as 1/2 raised to the positive 2 power. So the answer is 1/4. Likewise, 2 raised to the -3 power is 1/2 raised to the +3 power which is equal to 1/8. Note that a positive number raised to any power (whether positive or negative) will always be positive. Hope that helps. In the second step, we use the following: $9^{3/2}=9^{1/2\,+\,1}=9^{1/2}\cdot9^1=9\sqrt{9}$. Just be careful with $n$ even and the base negative (real-number roots may not exist). This becomes $3^{-3} = \frac{1}{3^3} = \frac{1}{27}$, so you do get the same answer. Odd and Even Whole Number Exponents. When a positive number is raised to an odd or even whole number, the result is always positive. Negative numbers, on the other hand, behave differently. When a negative number is raised to an even whole number power, the result will ALWAYS be a positive number. Raising a number to a negative fraction power. up vote 0 down vote favorite. I am doing a math problem where I need to raise 9 to the -3/2 power. I am unsure how this is done. I believe it's the equivalent of saying 2√9^-3, but I am unsure if this is true. If you can help me it would be much appreciated. Thank you for your time.
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