Question

(-7x^2/3y^4)^-3 * (9y^2/49x^4)-2

Answer 1

Ответ на вопрос : 5yx

Answer 2

To simplify the expression (-7x^(2/3)y^4)^(-3) * (9y^2/49x^4)^(-2), we'll first deal with the negative exponents by applying the properties of exponents. Remember that when you have a negative exponent, you can move the base to the opposite side of the fraction and change the exponent to positive. Here's how to simplify the expression step by step:

1. For the first part, (-7x^(2/3)y^4)^(-3):

   • Move the base to the denominator and change the exponent to positive: 1/(-7x^(2/3)y^4)^3

2. For the second part, (9y^2/49x^4)^(-2):

   • Move the base to the denominator and change the exponent to positive: 1/(9y^2/49x^4)^2

Now, let's simplify each part separately:

1. Simplify 1/(-7x^(2/3)y^4)^3: (1/(-7x^(2/3)y^4)^3)

   To simplify the exponent, raise everything inside the parentheses to the power of 3: (1/((-7x^(2/3))^3 * (y^4)^3))

   Calculate the cube of -7: (1/(-343 * x^(2/3)^3 * y^(4*3)))

   Simplify the exponents by multiplying: (1/(-343 * x^2 * y^12))

2. Simplify 1/(9y^2/49x^4)^2: (1/(9y^2/49x^4)^2)

   To simplify the exponent, raise everything inside the parentheses to the power of 2: (1/((9y^2/49x^4)^2))

   To square the expression inside, square the numerator and the denominator: (1/((9^2 * (y^2)^2) / (49^2 * (x^4)^2)))

   Calculate the squares and simplify: (1/((81 * y^4) / (2401 * x^8)))

Now that both parts are simplified, multiply them together:

(1/(-343 * x^2 * y^12)) * (1/((81 * y^4) / (2401 * x^8)))

To multiply fractions, simply multiply the numerators together and the denominators together:

(1 * 1) / (-343 * x^2 * y^12 * (81 * y^4) / (2401 * x^8))

Now, simplify the expression further:

(1 / (-343 * 81 * 2401)) * (1 / (x^2 * x^8 * y^12 * y^4))

Multiply the constants in the denominators:

(1 / (-7,319,187)) * (1 / (x^(2+8) * y^(12+4)))

Combine the exponents:

(1 / (-7,319,187)) * (1 / (x^10 * y^16))

So, the simplified expression is:

1 / (-7,319,187 * x^10 * y^16)