Questions: Use the laws of exponents to simplify. (2^(11/10))^(2/7) (2^(11/10))^(2/7) = □ (Simplify your answer. Type exponential notation with rational exponents.)

Solution Steps

To simplify the expression \(\left(2^{\frac{11}{10}}\right)^{\frac{2}{7}}\), we can use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Therefore, we multiply the exponents \(\frac{11}{10}\) and \(\frac{2}{7}\) together.

To simplify the expression \(\left(2^{\frac{11}{10}}\right)^{\frac{2}{7}}\), we use the power of a power property of exponents, which states that \((a^m)^n = a^{m \cdot n}\). Thus, we can rewrite the expression as: \[ 2^{\frac{11}{10} \cdot \frac{2}{7}} \]

Next, we calculate the new exponent by multiplying \(\frac{11}{10}\) and \(\frac{2}{7}\): \[ \frac{11}{10} \cdot \frac{2}{7} = \frac{22}{70} = \frac{11}{35} \]

Now, we can express the simplified form of the original expression: \[ \left(2^{\frac{11}{10}}\right)^{\frac{2}{7}} = 2^{\frac{11}{35}} \]

Final Answer