Question
Simplify.
-(f^-6)^-4
-(f^-6)^-4
Answers
Answered by
GPT 3.5
To simplify the expression -(f^-6)^-4, we start by simplifying the exponent inside the parenthesis.
An exponent of -6 means that we take the reciprocal of the base and also change the sign of the exponent.
-(f^-6)^-4 = -((1/f^6)^-4)
To simplify further, we apply the power of a power rule, which states that (a^m)^n = a^(m*n).
-((1/f^6)^-4) = -(1/(f^6 * -4))
Multiplying -4 with 6, we get -24.
-1/(f^6 * -4) = -1/(f^-24)
Finally, we simplify the expression within the parenthesis by making the exponent positive.
-1/(f^-24) = -f^24
Therefore, -(f^-6)^-4 simplifies to -f^24.
An exponent of -6 means that we take the reciprocal of the base and also change the sign of the exponent.
-(f^-6)^-4 = -((1/f^6)^-4)
To simplify further, we apply the power of a power rule, which states that (a^m)^n = a^(m*n).
-((1/f^6)^-4) = -(1/(f^6 * -4))
Multiplying -4 with 6, we get -24.
-1/(f^6 * -4) = -1/(f^-24)
Finally, we simplify the expression within the parenthesis by making the exponent positive.
-1/(f^-24) = -f^24
Therefore, -(f^-6)^-4 simplifies to -f^24.
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