find the product with the exponent in simplest form. then, identify the values of x and y.\n$6^{\frac{1}{3}}c…

find the product with the exponent in simplest form. then, identify the values of x and y.\n$6^{\frac{1}{3}}cdot6^{\frac{1}{4}} = 6^{\frac{x}{y}}$\n$x=square,y=square$

find the product with the exponent in simplest form. then, identify the values of x and y.\n$6^{\frac{1}{3}}cdot6^{\frac{1}{4}} = 6^{\frac{x}{y}}$\n$x=square,y=square$

Answer

Explanation:

Step1: Apply exponent - product rule

When multiplying two numbers with the same base (a^m\cdot a^n=a^{m + n}), here (a = 6), (m=\frac{1}{3}), and (n=\frac{1}{4}). So (6^{\frac{1}{3}}\cdot6^{\frac{1}{4}}=6^{\frac{1}{3}+\frac{1}{4}}).

Step2: Calculate the sum of the fractions

Find a common - denominator for (\frac{1}{3}+\frac{1}{4}). The common denominator of 3 and 4 is 12. Then (\frac{1}{3}+\frac{1}{4}=\frac{1\times4}{3\times4}+\frac{1\times3}{4\times3}=\frac{4 + 3}{12}=\frac{7}{12}). So (6^{\frac{1}{3}}\cdot6^{\frac{1}{4}}=6^{\frac{7}{12}}).

Answer:

(x = 7), (y = 12)