(9/25)^-3/2
I know it's 125/27 but I need it with a whole number and a fraction
Oh, please. you can extract roots and raise powers, but can't convert a fraction to a mixed number?
125/27 = 4.6 something, so it will be 4 + some fraction.
4*27 = 108, so
125/27 = 108/27 + 17/27 = 4 17/27
Ummm I actually do noe but I just wanted to make sure. Plus I've finished my work already .
To calculate the value of (9/25)^(-3/2), you need to follow these steps:
Step 1: Start by calculating the reciprocal of 9/25.
The reciprocal of a fraction is obtained by flipping the numerator and the denominator. So, the reciprocal of 9/25 is 25/9.
Step 2: Raise the reciprocal (25/9) to the power of -3/2.
To raise a number to a negative power, you can take the reciprocal of the number and raise it to the positive power. In this case, we can take the reciprocal of 25/9, which is 9/25, and raise it to the power of 3/2.
Step 3: Calculate (9/25)^(3/2).
When you raise a fraction to an exponent, you need to raise both the numerator and the denominator to the power separately. So, raising 9/25 to the power of 3/2 is equivalent to raising 9^3 to the power of 1/2 divided by 25^3 raised to the power of 1/2.
Step 4: Calculate 9^3 and 25^3.
9^3 means 9 raised to the power of 3, which is 9 * 9 * 9 = 729. Similarly, 25^3 means 25 raised to the power of 3, which is 25 * 25 * 25 = 15625.
Step 5: Simplify the expression (9^3)^(1/2) / (25^3)^(1/2).
Since both the numerator and the denominator are raised to the same power, you can simplify the expression by taking the square root of each term separately. The square root of 9^3 is √(9^3) = √729 = 27, and the square root of 25^3 is √(25^3) = √15625 = 125.
Step 6: Divide the values obtained in step 5 to get the final result.
27/125 is the final result of the expression (9/25)^(-3/2).
Therefore, the value of (9/25)^(-3/2) is 27/125.