Online Rational Exponents Tutors

Online Rational Exponents Tutors 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.