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

Question

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

x
2
1
​

=
x
a

Answer 1

To evaluate the left hand side, we first have to rewrite the expression in exponential form:

x^(2/3) * x^(1/2)

When multiplying two numbers with the same base, you add the exponents. So,

x^(2/3) * x^(1/2) = x^(2/3 + 1/2) = x^(4/6 + 3/6) = x^(7/6)

Therefore, the value of a is 7/6.