Question

((3/4)^0)^-0.5-7.5*4^-3/2-(-2)^-4+81^0.25

Answer 1

1. Вычислить ((3/4)^0)^-0.5 *7.5 *4^(3/2) – (-2)^(-4) +81^0.25

Answer 2

Let's solve the expression step by step:

Step 1: ((3/4)^0)^(-0.5) Any number (except 0) raised to the power of 0 is always 1. So, ((3/4)^0) equals 1. Now, we have 1^(-0.5), and any number raised to the power of -0.5 is its reciprocal raised to the power of 0.5. Reciprocal of 1 is also 1, so 1^(-0.5) equals 1.

Step 2: -7.5*4^(-3/2) Let's calculate the second term first, 4^(-3/2). 4^(-3/2) is the same as 1/(4^(3/2)). The square root of 4 is 2, so 4^(3/2) is 4^1.5 = 2^3 = 8. So, 4^(-3/2) is 1/8. Now, we can calculate the second term as -7.5 * (1/8) = -7.5/8.

Step 3: -(-2)^(-4) In this case, the double negative will cancel out, making it equivalent to (-2)^(-4). The negative exponent means we need to take the reciprocal, so (-2)^(-4) is 1/(-2)^4 = 1/16.

Step 4: 81^(0.25) 81^(0.25) is the same as taking the 4th root of 81. The 4th root of 81 is 3, as 3^4 = 81.

Now, let's sum up all the results from the steps:

1 + (-7.5/8) + (1/16) + 3 = 1 + (-0.9375) + 0.0625 + 3 = 3.125

So, the final result of the expression is 3.125.