Question

The expression (5x^4y^−5/6)^5(4y²)²/3 equals nxr/yt where n, the coefficient, is: r, the exponent of x, is: t, the exponent of y, is:

Answer 1

To simplify the expression, apply the rules of exponents. The coefficient is 3125, the exponent of x is 20, and the exponent of y is -19/6.

Step-by-step explanation:

To simplify the expression, we will use the rules of exponents.

First, we need to apply the power of a power rule for the first part of the expression: (5x^4y^(-5/6))^5 = 5^5 * x^(4*5) * y^(-5/6 * 5) = 3125x^20 * y^(-25/6).

Next, we simplify the second part of the expression: (4y^2)^(2/3) = 4^(2/3) * y^(2 * 2/3) = 2.5198 * y^(4/3).

Finally, multiplying the two simplified parts together gives us: 3125x^20 * y^(-25/6) * 2.5198 * y^(4/3). Combining the y terms by adding exponents, we get: 3125x^20 * y^(-25/6 + 4/3) = 3125x^20 * y^(-27/6 + 8/6) = 3125x^20 * y^(-19/6).

The coefficient is 3125, the exponent of x is 20, and the exponent of y is -19/6.

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