Simplify. Write with positive exponents. Assume that all variables represent positive real numb (p^1/7p^9/14p^1/2)/((p^12))^(-1/7) (p^1/7p^9/14p^1/2)/((p^12))^(-1/7)= square (Simplify your answer. Type exponential notation with positive exponents.)

To simplify the expression, we can use the properties of exponents.<br /><br />Given expression: $\frac {p^{1/7}p^{9/14}p^{1/2}}{(p^{12})^{-1/7}}$<br /><br />Step 1: Combine the exponents in the numerator.<br />$p^{1/7}p^{9/14}p^{1/2} = p^{1/7 + 9/14 + 1/2} = p^{1/7 + 9/14 + 7/14} = p^{1/7 + 16/14} = p^{1/7 + 8/7} = p^{9/7}$<br /><br />Step 2: Simplify the denominator.<br />$(p^{12})^{-1/7} = p^{12 \cdot (-1/7)} = p^{-12/7}$<br /><br />Step 3: Divide the numerator by the denominator.<br />$\frac {p^{9/7}}{p^{-12/7}} = p^{9/7 - (-12/7)} = p^{9/7 + 12/7} = p^{21/7} = p^Therefore, the simplified expression is $p^3$.