Simplify the expression below. Express the answer so that all exponents are positive. Whenever an exponent is 0 or negative, we assume that the base is not 0.
(7x^-5/4y^-5)^-6
Is the answer 4096x^30/117649y^30
yes
To simplify the expression (7x^-5/4y^-5)^-6, we can start by working on the negative exponents and putting them in the denominator. Remember that a negative exponent in the numerator becomes positive in the denominator.
So, we can rewrite the expression as:
(7/(x^5 * y^5))^6
Now, to simplify further, we need to raise both the numerator and the denominator to the power of 6. We do this by raising each term individually to the power of 6:
(7^6)/(x^5)^6 * (y^5)^6
Simplifying the powers:
(7^6)/(x^30) * (y^30)
Now, we can simplify the expression by multiplying the numbers and combining the exponents:
(117,649)/(x^30) * (y^30)
Therefore, the simplified expression is:
117,649x^30/y^30