Simplify the expression:
(x^9y^-4)^6
x^54/y^24
Is this correct?
Yes it is.
(x^9 * y^-4)^6 = x^54 * y^(-24)
To simplify the expression (x^9y^-4)^6, you need to apply the power rule for exponents. In this case, you raise both the base, x, and the exponent, 9, to the power of 6. Similarly, you raise the base, y, and the exponent, -4, to the power of 6.
Applying the power rule for exponents, we have:
(x^9y^-4)^6 = x^(9*6)y^(-4*6)
Simplifying the exponents, we get:
x^54y^-24
However, to fully simplify the expression, we need to bring the negative exponent, y^-24, to the denominator. When an exponent is negative, it indicates that the base should be moved to the denominator.
Simplifying further, we have:
x^54/y^24
Therefore, your simplification, x^54/y^24, is correct.