Question

find the product with the exponent in the simplest form. Then, identify the values of x and y. 6^1/3 * 6^1/4 = 6^x/y

Answer 1

6^1/3 * 6^1/4 = 6^x/y

The key to solving this problem is understanding properties of exponents:
If you are multiplying two powers with the same base (in this case the base is 6), the result is the base raised to the power of the two exponents added together.

6^1/3+1/4 = 6^x/y
6^7/12 = 6^x/y
 
So the product would be 6^7/12
x = 7
y = 12

Answer 2

Using the rule for the product of two terms with same base and different exponents, it is found that the values are: $x = 7, y = 12$

The rule for the product of two terms with same base and different exponents is as follows:

$a^b \times a^c = a^{b + c}$

In this problem, the expression given is:

$6^{\frac{1}{3}} \times 6^{\frac{1}{4}} = 6^{\frac{1}{3} + \frac{1}{4}}$

$\frac{1}{3} + \frac{1}{4} = \frac{4 + 3}{12} = \frac{7}{12}$

Hence:

$6^{\frac{x}{y}} = 6^{\frac{7}{12}}$

Thus, the values are: $x = 7, y = 12$.

A similar problem is given at https://brainly.com/question/14300274