### Instruction: The expression $\dfrac{\sqrt[4]{7}}{\sqrt[3]{7}}$ equals 7 raised to what power?### Response: I need to find an exponent x such that $\dfrac{\sqrt[4]{7}}{\sqrt[3]{7}} = 7^x$.
To make the bases match, I can rewrite the radicals as fractional exponents: $\dfrac{7^{1/4}}{7^{1/3}} = 7^x$.
Using the quotient rule of exponents, I can subtract the exponents in the numerator and denominator: $7^{1/4 - 1/3} = 7^x$.
To subtract the fractions, I need a common denominator: $7^{\dfrac{3}{12} - \dfrac{4}{12}} = 7^x$.
Simplifying, I get: $7^{-1/12} = 7^x$.