can a base be negative at the same time as my exponent?
how will you solve this one?
-6 ^-3
as long as the exponent is an integer, the base can be negative. Negative exponents just mean that you take the reciprocal:
(-6)^(-3) = 1/(-6)^3 = 1/-216 = -1/216
awesome.. I wasn't sure about the negative sign..:)
To determine whether a base can be negative while the exponent is negative, let's understand the properties of exponents.
The exponent of a number represents how many times that number should be multiplied by itself. In the case of a negative exponent, it indicates taking the reciprocal or inverse of the base raised to the positive value of the exponent.
Now, let's solve the specific expression you provided: -6^-3.
To solve this, we need to apply the rules of exponentiation. Since the base (-6) is negative and the exponent (-3) is also negative, we have a negative number raised to a negative exponent.
When you have a negative base raised to a negative exponent, it is equivalent to flipping the fraction and changing the sign of both the base and the exponent.
So, -6^-3 can be rewritten as (-1/6)^3.
Therefore, -6^-3 is equivalent to (-1/6)^3. We have converted it into a positive exponent by flipping the fraction.