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

Question

x, start superscript, start fraction, 5, divided by, 4, end fraction, end superscript, x, start superscript, start fraction, 3, divided by, 2, end fraction, end superscript, equals, x, to the power a
x
4
5
​

x
2
3
​

=
x
a

Answer 1

To evaluate the left hand side of the equation, we need to simplify the expressions:

x^(5/4) * x^(3/2)

When multiplying with the same base (x in this case), we add the exponents:

x^(5/4 + 3/2)

Now we need to find a common denominator:

5/4 = 10/8
3/2 = 12/8

Adding the fractions together, we get:

x^(10/8 + 12/8)
x^(22/8)

Simplifying the exponent by dividing both the numerator and denominator by 2:

x^(11/4)

Therefore, the left hand side of the equation simplifies to x^(11/4). So, the value of a in the equation x^(11/4) = x^a is 11/4.