(-10)^5 is a power with a base of -10 and an exponent of 5. To determine whether the value of this power is positive or negative, we need to consider the following:
When the base is negative and the exponent is odd, the result is negative.
When the base is negative and the exponent is even, the result is positive.
In this case, the base (-10) is negative and the exponent (5) is odd. Therefore, the value of (-10)^5 is negative.
Similarly, let's determine the values of the other powers:
(-3)^4: The base (-3) is negative and the exponent (4) is even, so the value of (-3)^4 is positive.
(-2)^9: The base (-2) is negative and the exponent (9) is odd, so the value of (-2)^9 is negative.
(-1)^2: The base (-1) is negative and the exponent (2) is even, so the value of (-1)^2 is positive.
(-6)^3: The base (-6) is negative and the exponent (3) is odd, so the value of (-6)^3 is negative.
(-4): Since this is not a power, we can directly determine its value. The number (-4) is negative.
To summarize:
(-10)^5 is negative.
(-3)^4 is positive.
(-2)^9 is negative.
(-1)^2 is positive.
(-6)^3 is negative.
(-4) is negative.
I hope this helps! Let me know if you have any further questions.
Answer:
Result at the end of explanation.
Step-by-step explanation:
There's a fairly simple rule here (for when the base is a real number). If the exponent is even, then the result is even whether the base is positive or negative. If the exponent is odd, the result is negative if the base is negative but positive if the base is positive. What about if the exponent is 0 then? Then the result is always 1.
Negative
[tex](-10)^{5} \\(-2)^{9} \\(-6)^{3} \\-4[/tex]
Positive
[tex](-3)^{4}\\(-1)^{2}[/tex]
