To simplify the expression \((29)^{\frac{1}{2}} \cdot (29^5)^{\frac{3}{2}}\) using the laws of indices, we can apply the following steps:
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Apply the power of a power rule: When raising a power to a power, you multiply the exponents. Thus, for the second term \((29^5)^{\frac{3}{2}}\), we have: \[ (29^5)^{\frac{3}{2}} = 29^{5 \cdot \frac{3}{2}} = 29^{\frac{15}{2}}. \]
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Combine the powers: Now we have: \[ (29)^{\frac{1}{2}} \cdot (29)^{\frac{15}{2}}. \] Using the rule for multiplying powers with the same base (add the exponents), we have: \[ 29^{\frac{1}{2} + \frac{15}{2}} = 29^{\frac{1 + 15}{2}} = 29^{\frac{16}{2}} = 29^8. \]
Therefore, the simplified expression is: \[ \boxed{29^8}. \]