Evaluate the left hand side to find the value of aa in the equation in simplest form.

Question

start fraction, x, start superscript, start fraction, 5, divided by, 4, end fraction, end superscript, divided by, x, start superscript, one sixth, end superscript, end fraction, equals, x, to the power a
x
6
1
​


x
4
5
​


​
=
x
a

Answer 1

To evaluate the left-hand side of the equation in simplest form, we need to simplify it first.

Starting with the left side of the equation:

(x^(5/4)) / x^(1/6)

When dividing terms with the same base, we subtract the exponents:
x^(5/4 - 1/6)
x^(5/4 - 2/12)
x^(5/4 - 1/6)
x^(5/4 - 2/12)

Now, find a common denominator:
x^(15/12 - 2/12)
x^(13/12)

x^(13/12)

Therefore, the left-hand side of the equation is x^(13/12). Now, the equation is:

x^(13/12) = x^a

Since the bases on both sides are equal, the exponents must also be equal. Therefore, we have:

13/12 = a

Thus, the value of a is 13/12.