1. To simplify 49^(3/2), we can rewrite it as (sqrt(49))^3. The square root of 49 is 7, so we have 7^3, which is equal to 343. Therefore, your answer of 343 is correct.
2. To simplify 5^(x^25y^125), we can break it down into separate terms. Since we have x raised to a power and y raised to a power, we can apply the product of powers rule. The simplified expression would be 5^x * 5^(25y^125).
3. The polynomial 5x - 2x + 8x^2 - 7 can be rearranged in standard form by arranging the terms in descending order of their degrees. So the standard form of the polynomial would be 8x^2 + 5x - 2x - 7.
The leading coefficient is the coefficient of the term with the highest degree, which is 8. Therefore, your answer of -2 is incorrect. The correct answer is 8.
4. The polynomial 5x^2 + 9x + 1 has three terms and the highest power of x is 2. Therefore, it is classified as a quadratic trinomial. Your answer is correct.
5. The area of the cage can be found by substituting the width, w, into the given polynomial. If the width is 15 feet, we can replace w with 15 in the polynomial -2x^2 + 100w.
So the area of the cage would be -2x^2 + 100(15), which simplifies to -2x^2 + 1500.
Therefore, your answer of 1,050 feet is incorrect. The correct answer is -2x^2 + 1500 square feet.
6. To add (5x^2 - 2x + 9) + (2x^2 - 4), we combine like terms.
The like terms are the ones with the same power of x. So, the sum would be (5x^2 + 2x^2) + (-2x) + 9 + (-4).
This simplifies to 7x^2 - 2x + 5. Therefore, your answer is incorrect.
The correct answer is 7x^2 - 2x + 5.
7. To subtract (10a^2 - 6a) - (7a^2 - 8a), we distribute the negative sign to each term inside the second parentheses.
This gives us 10a^2 - 6a - 7a^2 + 8a.
Next, we combine like terms. The like terms are the ones with the same power of a.
So, the simplifed expression would be (10a^2 - 7a^2) + (-6a + 8a).
This further simplifies to 3a^2 + 2a. Therefore, your answer is incorrect.
The correct answer is 3a^2 + 2a.
8. To multiply (-5rs^4)(3r^5s^2), we use the product of powers rule and multiply the coefficients and the variables separately.
The multiplication of the coefficients gives us (-5)(3) = -15.
The multiplication of the variables gives us (r*r^5)(s^4*s^2) = r^(1+5) * s^(4+2) = r^6 * s^6.
Therefore, the final answer is -15r^6s^6. Your answer is correct.
9. To find (3x - 4)^2, we can use the formula for binomial squared: (a - b)^2 = a^2 - 2ab + b^2.
Using the formula, we have (3x)^2 - 2(3x)(4) + (4)^2.
This simplifies to 9x^2 - 24x + 16. Therefore, your answer of 6x^2 - 24x + 8 is incorrect.
The correct answer is 9x^2 - 24x + 16.
10. To multiply (2x + 4)(2x - 4), we can use the formula for multiplying two binomials: (a + b)(a - b) = a^2 - b^2.
Using the formula, we have (2x)^2 - (4)^2 = 4x^2 - 16.
Therefore, your answer of 4x^2 - 8 is incorrect.
The correct answer is 4x^2 - 16.