Question

(8a3÷27x-3)2/3x(64a3÷27x-3)-2/3​

Answer 1

Answer:

(8a^3 ÷ 27x^-3)^2/3 * (64a^3 ÷ 27x^-3)^-2/3

= (2a * 3x)^[3*2/3] * (4a * 3x)^[3*-2/3]

= (6ax)^2 * (12ax)^-2

= 6a^2x^2/

12a^2x^2

= 1/2

Step-by-step explanation:

Answer 2

Answer:

The correct answer is : 1/4

Step-by-step explanation:

(8a^3 ÷ 27x^-3)^2/3 * (64a^3 ÷ 27x^-3)^-2/3

Let's simplify the above expression step by step:

First, we can simplify the terms inside the parentheses:

8a^3 ÷ 27x^-3 = (2a ÷ 3x)^3

64a^3 ÷ 27x^-3 = (4a ÷ 3x)^3

Now we can substitute these simplified expressions back into the original expression:

[(2a ÷ 3x)^3]^(2/3) * [(4a ÷ 3x)^3]^(-2/3)

Next, we can use the property of exponents that states that (a^m)^n = a^(mn) to simplify each of the exponents inside the parentheses:

(2a ÷ 3x)^(32/3) * (4a ÷ 3x)^(3*(-2/3))

Simplifying the exponents gives:

(2a ÷ 3x)^2 * (4a ÷ 3x)^(-2)

Next, we can use the property of exponents that states that a^-n = 1/a^n to move the negative exponent in the second term to the numerator:

(2a ÷ 3x)^2 * (3x ÷ 4a)^2

Now we can expand each term using the square of a binomial formula, which states that (a + b)^2 = a^2 + 2ab + b^2:

(4a^2 ÷ 9x^2) * (9x^2 ÷ 16a^2)

The x^2 and a^2 terms cancel out, leaving:

4 ÷ 16 = 1 ÷ 4

Therefore, the final simplified expression is:

1/4.

To learn more about Division, visit:

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To learn more about Algebraic geometry, visit:

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