(6q^6)^-4
When I worked this I got 1/1296q^24.
One of the choices given was
1/1296q^-24. The other choices were:
6q^1296, 1296q^2, 6q^-24. Is the answer any of these choices?
It's most probably the last one as you multiply the exponents together.
To solve the expression (6q^6)^-4, we can follow the order of operations, which is to simplify the exponent first and then apply the reciprocal.
Step 1: Simplify the exponent inside the parentheses.
To simplify the exponent, we need to multiply the exponent outside the parentheses by the exponent inside the parentheses.
(6q^6)^-4 = 6^(-4) * (q^6)^(-4)
Step 2: Simplify the first term, which is 6^(-4).
To simplify the negative exponent, we can rewrite it as the reciprocal of the positive exponent.
6^(-4) = 1 / 6^4 = 1 / 1296
Step 3: Simplify the second term, which is (q^6)^(-4).
To simplify the exponent, we need to multiply the exponents together.
(q^6)^(-4) = q^(6*(-4)) = q^(-24)
Step 4: Combine the simplified terms.
Now, we can combine the simplified terms from step 2 and step 3.
(6q^6)^-4 = 1 / 1296 * q^(-24) = 1/1296q^24
Therefore, the given expression simplifies to 1/1296q^24.
Out of the choices given, the correct answer is indeed 1/1296q^24. None of the other choices (6q^1296, 1296q^2, 6q^-24) match the simplification of the original expression.