I have no idea how to do these please help(:

evaluate each of the following

1. 81^-1/4 (81 to the negative power of one fourth)
2. 125^2/3
3. 64^-3/2
4. 4^3/2
answers and work please

81^-(1/4)

= 1/81^(1/4)
well 81=9*9 which is 3*3*3*3
so
3
so the answer is 1/3

125 = 5*5*5
so
125^(1/3) = 5
5^2 = 25
so the answer is 25

I bet you know 4^(1/2)
and I bet you can cube that.

Of course, I'd be happy to help you with these! To evaluate each of the given expressions, we'll need to understand a few concepts of exponentiation and fractional exponents.

1. To evaluate 81^(-1/4), we need to remember that a negative exponent signifies taking the reciprocal of the base. In this case, the base is 81. So, we first find the reciprocal of 81, which is 1/81. Then, we raise it to the power of 1/4. To simplify further, we can use the fact that the fourth root of 1/81 is equal to 1/(fourth root of 81). The fourth root of 81 is 3 since 3^4 = 81. Therefore, we have 1/(3^1) which simplifies to 1/3.

2. For 125^(2/3), we need to understand that an exponent raised to a fractional power involves taking the root of the base. Here, we have the cube root (3√) of 125 raised to the power of 2. The cube root of 125 is 5 since 5^3 = 125. Therefore, we have 5^2 which equals 25.

3. To evaluate 64^(-3/2), we follow the same steps as in question 1. The base is 64, so we find its reciprocal, which is 1/64, and then raise it to the power of -3/2. To simplify further, we can use the fact that the square root (2√) of 1/64 is equal to 1/(square root of 64). The square root of 64 is 8 since 8^2 = 64. Therefore, we have 1/(8^3) which is equal to 1/512.

4. Lastly, for 4^(3/2), we can evaluate it by taking the square root of the base 4, which is equal to (square root of 4)^3. The square root of 4 is 2, so we have 2^3 which equals 8.

Therefore, the evaluations are:
1. 81^(-1/4) = 1/3
2. 125^(2/3) = 25
3. 64^(-3/2) = 1/512
4. 4^(3/2) = 8