1. Find the GCF and LCM of 1589 and 105 2 = Express 720 as prime Factorization form 3= Express (1)/(110) in tue Exponential from 4 Simplify (-243) (1)/(5) 5 The multiplicative inversue of (3 sqrt(4))/(1-sqrt(6))

1. To find the GCF (Greatest Common Factor) and LCM (Least Common Multiple) of 1589 and 105:<br /><br />- Prime factorization of 1589: \( 1589 = 1 \times 1589 \) (since 1589 is a prime number)<br />- Prime factorization of 105: \( 105 = 3 \times 5 \times 7 \)<br /><br />Since there are no common factors other than 1, the GCF is 1.<br /><br />To find the LCM:<br />\[ \text{LCM}(1589, 105) = \frac{1589 \times 105}{\text{GCF}} = \frac{1589 \times 105}{1} = 166845 \]<br /><br />So, the GCF is 1 and the LCM is 166845.<br /><br />2. Express 720 as prime factorization form:<br />\[ 720 = 2^4 \times 3^2 \times 5 \]<br /><br />3. Express \( \frac{1}{110} \) in exponential form:<br />\[ \frac{1}{110} = 110^{-1} \]<br /><br />4. Simplify \( (-243)^{\frac{1}{5}} \):<br />\[ (-243)^{\frac{1}{5}} = -3 \]<br />(Note: This assumes the principal real root.)<br /><br />5. The multiplicative inverse of \( \frac{3 \sqrt{4}}{1-\sqrt{6}} \):<br /><br />First, simplify the expression:<br />\[ \frac{3 \sqrt{4}}{1-\sqrt{6}} = \frac{3 \times 2}{1-\sqrt{6}} = \frac{6}{1-\sqrt{6}} \]<br /><br />The multiplicative inverse is:<br />\[ \left( \frac{6}{1-\sqrt{6}} \right)^{-1} = \frac{1-\sqrt{6}}{6} \]