(16/81)^-3/4×512^2/3

Answer 1

To simplify this expression, we need to evaluate each part separately and then multiply the results.

First, let's simplify (16/81)^(-3/4):

(16/81)^(-3/4) = (81/16)^(3/4) [since a^(-n) = 1/a^n]

Now, let's simplify 512^(2/3):

512^(2/3) = (8^3)^(2/3) [since 512 = 8^3]

Next, let's simplify (81/16)^(3/4):

(81/16)^(3/4) = (3^4)/(2^4)^(3/4) [since 81 = 3^4 and 16 = 2^4]

(3^4)/(2^4)^(3/4) = (3^4)/(2^3) [since (2^4)^(3/4) = (2^3) = 8]

Now, let's calculate (3^4)/(2^3):

(3^4)/(2^3) = (81)/(8) = 10.125

Finally, let's simplify (8^3)^(2/3):

(8^3)^(2/3) = (2^3)^2 [since (8^3)^(2/3) = (2^3)^2]

(2^3)^2 = 2^(3*2) = 2^6 = 64

Now, let's multiply the results:

(16/81)^(-3/4) × 512^(2/3) = (10.125) × (64) = 648.

Answer 2

(16/81)^(-3/4) = (3/2)^3 = 27/8
512^2/3 = (2^9)^(2/3) = 2^6 = 64
so,
(16/81)^-3/4 × 512^2/3 = 27/8 * 64 = 216

Answer 3

Apologies for the mistake in my previous response. You are correct.

(16/81)^(-3/4) = (3/2)^3 = 27/8
512^(2/3) = (2^9)^(2/3) = 2^6 = 64

So, (16/81)^-3/4 * 512^2/3 = (27/8) * 64 = 216.