Raising Fractions to a Power
The calculation is carried out according to the following rules:
When raising a fraction to a power, it is necessary to raise both the numerator and the denominator to the given power.
How to raise a simple fraction to a power:
For example, let's take a fraction 3/5; and raise it to the power of 2.According to the rule, we raise both the numerator and the denominator to the second power, that is, 3 to the power of 2, and 5 to the power of 2, and find the answer 9/25.
Raising a mixed number to a power:
To raise a mixed number to a power, first convert the mixed number to an improper fraction.For example, let's take a fraction 34/5; and convert it to an improper fraction. To do this, we multiply the denominator by the whole number and add the numerator, in our case, it will be 5*3+4=19 is the number that goes into the numerator of our fraction, and the denominator remains as 5.
The final fraction will look like this
19/5
.
After converting the mixed number to an improper fraction, we raise both the numerator and the denominator to the required power, in the same way as we did with a simple fraction.
Raise 19/5; to the third power, and by calculating, we get: 361/25
, Calculate the whole part of the fraction, and get the answer: 14 11/25.
How to raise a negative fraction to a power:
Raising a negative fraction is almost the same as raising a positive fraction to a power.For calculation, also raise both the numerator and the denominator to the power, and see if the power is even, for example, 4, then the minus sign in front of the fraction disappears, if it's odd, for example, 5, then the minus sign remains.