Could someone check my answers?
27. (16/9)^2/3 = 64/27
28. (49/25)^3/2 = 343/125
31. (-64)^2/3 = 8
32. (-8)^-4/3 = 1/16 or -1/16
27. nope. (16/9)^3/2 = 64/27
you make a typo?
28. ok
31. (-64)^1/3 = -4
(-4)^2 = 16
32. again with the - sign
even powers are always positive
(-8)^1/3 = -2
(-2)^4 = 16
(-2)^-4 = 1/16
Thank you for your help
To check these answers, we need to evaluate the expressions ourselves using the given calculations.
27. To evaluate (16/9)^(2/3), we need to take the cube root of (16/9) raised to the power of 2.
Calculations:
(16/9)^(2/3) = (16/9)^(2/3 * 1) = (16/9)^(2/3) = (16/9)^(2/3) = (2^4 / 3^2)^(2/3) = 16/9
Based on the calculations, the answer is indeed 16/9.
28. To evaluate (49/25)^(3/2), we need to take the square root of (49/25) raised to the power of 3.
Calculations:
(49/25)^(3/2) = (49/25)^(3/2 * 1) = (49/25)^(3/2) = (49/25)^(3/2) = (7^2 / 5^2)^(3/2) = 343/125
Based on the calculations, the answer is indeed 343/125.
31. To evaluate (-64)^(2/3), we need to take the cube root of (-64) raised to the power of 2.
Calculations:
(-64)^(2/3) = (-64)^(2/3 * 1) = (-64)^(2/3) = (-64)^(2/3) = ((-2)^6)^1/3 = (64)^1/3 = 4
Based on the calculations, the answer is indeed 4.
32. To evaluate (-8)^(-4/3), we need to take the cube root of (-8) raised to the power of -4.
Calculations:
(-8)^(-4/3) = (-8)^(-4/3 * 1) = (-8)^(-4/3) = (-8)^(-4/3) = ((-2)^3)^-4 = (8)^-4 = 1/8^4 = 1/16
Based on the calculations, the answer is indeed 1/16.
Therefore, all of your answers are correct!