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p raised to the (x/y)th power is the yth root of px or equivalently (yth root of p)x. If you do not have a calculator, then the second of these is generally simpler because you are not dealing with cery large numbers.
For example, 25(3/2) can be calculated as the square root of 253 or the square root of 15625. Some people would lose hope when faced with that. But change the order of operation and find the cube of the square root of 25. The square root of 25 is 5 and cubing that is easy: 125.
Note that in questions dealing with indices, it is cpmmon to ignore the second (negative) square root.
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What if the problem is a fraction with a negative exponent?
Flip the fraction top-to-bottom, and delete the minus sign from the exponent.
Can you have a fraction as an exponent?
Yes.
Why can an exponent be a fraction or decimal?
Why not? An exponent is just like any other number.
Can a exponent be a fraction or decimal?
It can be either.
How do you solve a problem that has a variable with an exponent?
multiply
How do you solve a exponent?
Exponent is repeated multiplication
What if the problem is a fraction with a negative exponent?
Flip the fraction top-to-bottom, and delete the minus sign from the exponent.
Can you have a fraction as an exponent?
Yes.
What is the reciprocal of a negative exponent when the exponent is a fraction?
The reciprocal of a^(-x/y) is 1/a^(x/y). The fact that the exponent is a fraction makes no difference.
Why can an exponent be a fraction or decimal?
Why not? An exponent is just like any other number.
What does a negative exponent produce?
A fraction
Can a exponent be a fraction or decimal?
It can be either.
How do you solve a problem that has a variable with an exponent?
multiply
Do you see a relationship between the exponents of the base and the exponent of the product?
The exponent of the base is a step to solve the problems now the exponent of the product will also adjust a step to solve the equation but it contains more cooperative need.
Why is a number to a negative exponent a fraction?
Because a number to the exponent 0 = 1 and any lesser exponent decreases the value.
Why is a negitave exponent put into fraction form?
A negative exponent is put into fraction form because it is a way of writing powers of fractions or decimals.
If the coefficient of the expression ax is in fraction and the exponent is positive the expression will be a polynomial?
Not necessarily. If the exponent is not an integer then it is not a polynomial.
