simplify (−5)^5/(−5)^−6, Enter your answer as a number to a power, using the ^ symbol to indicate an exponent. For example, if you get 42 to the 53 power type it like this: 42^53
Well, well, well, it seems we have some exponent fun here! Let's dive in and simplify this expression.
Okay, let's start by simplifying the numerator, which is (-5)^5. Now, when we raise a negative number to an odd power, the result is negative. So (-5)^5 is equal to -5 times -5 times -5 times -5 times -5.
That gives us -5 * -5 * -5 * -5 * -5 = -3125.
Now let's move on to the denominator, which is (-5)^-6. Remember, when we raise a negative number to a negative power, it becomes positive. So (-5)^-6 is equal to 1 divided by (-5)^6.
Now, we know that (-5)^6 is positive since the number inside the parentheses is raised to an even power. So the denominator simplifies to 1 divided by (−5)^6.
Finally, let's put it all together. We have -3125 divided by (1/(−5)^6). Now, dividing by a fraction is the same as multiplying by its reciprocal. So we can rewrite the expression as -3125 times ((−5)^6/1).
Simplifying further, we get -3125 times (−5)^6.
And voila! That's the simplified expression. So the answer is -3125 times (−5)^6.
To simplify (-5)^5/(-5)^-6, we can apply the rule of exponents which states that when dividing two exponentiated numbers with the same base, we subtract the exponents.
Therefore, we have (-5)^5/(-5)^-6 = (-5)^(5-(-6)) = (-5)^11.
Hence, the simplified expression is -5^11.
To simplify the expression (-5)^5 / (-5)^(-6), we can use the rule of exponents which states that when dividing two powers with the same base, we can subtract the exponents. Therefore, (-5)^5 / (-5)^(-6) is equal to (-5)^(5 - (-6)).
Simplifying further, (-5)^(5 - (-6)) becomes (-5)^(5 + 6).
Adding the exponents, (-5)^(5 + 6) simplifies to (-5)^11.
So the simplified form of (-5)^5 / (-5)^(-6) is (-5)^11.
x^a / x^b = x^(a-b)
so we have
(-5)^(5-(-6)) = (-5)^11 = -5^11