Rational Exponents

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Exponent is the degree or the power of a given number or variable. If the exponent or the degree of a given variable or number is a fraction then it is called as rational exponent. There are many algebraic and numerical questions which involve solving rational exponents. If there is an expression x1/n here x is the variable and 1/n is called the nth root of x. For a given expression xm/n, m is the whole number and 1/n is the nth root of the variable x. 
 
Example 1: Solve the given equation (x1/4 )*(x3/4) = xy/2. Find y?

Solution: Given is the equation (x1/4 )*(x3/4) = xy/2

Using the power rule for multiplication xm * xn = xm+n

This gives (x1/4 )*(x3/4) = x (1/4 + 3/4) = x1.

Now x1 = xy/2

Since the bases of the equation are the same equate the exponents of x.

1 = y/2 (Multiplying both sides by 2.)

This give y = 2.
 
Example 2: Solve the given equation (x2/3 )*(x)/x7/3  = xy/3. Find y?

Solution: In the given equation (x2/3 )*(x)/x7/3  = xy/3

Using the power rule for multiplication xm * xn = xm+n

This gives (x2/3 )*(x) = x (1+ 2/3) = x5/3.

Using the power rule for division xm / xn = xm-n

(x)5/3/(x)/x7/3 = x5/3 – 7/3 = x-2

Now x-2 = xy/3

Since the bases of the equation are the same equate the exponents of x.

-2 = y/3  (Multiplying both sides by 3.)

This give y = -6.

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