1. Find the value of: \( \begin{array}{ll}\text { (a) } 3^{5} \times 3^{5} & \text { (b) } 9^{4} \times \frac{1}{9^{3}}\end{array} \)

Calculate the value by following steps: - step0: Calculate: \(9^{4}\left(\frac{1}{9^{3}}\right)\) - step1: Remove the parentheses: \(9^{4}\times \frac{1}{9^{3}}\) - step2: Reduce the numbers: \(9\times 1\) - step3: Simplify: \(9\) Calculate or simplify the expression \( 3^5 * 3^5 \). Calculate the value by following steps: - step0: Calculate: \(3^{5}\times 3^{5}\) - step1: Multiply: \(3^{5+5}\) - step2: Add the numbers: \(3^{10}\) - step3: Evaluate the power: \(59049\) Let's solve the two parts step by step: ### (a) \( 3^{5} \times 3^{5} \) Using the property of exponents that states \( a^m \times a^n = a^{m+n} \), we can simplify: \[ 3^{5} \times 3^{5} = 3^{5+5} = 3^{10} \] Now, calculating \( 3^{10} \): \[ 3^{10} = 59049 \] So, the value of \( 3^{5} \times 3^{5} \) is **59049**. ### (b) \( 9^{4} \times \frac{1}{9^{3}} \) We can rewrite \( \frac{1}{9^{3}} \) as \( 9^{-3} \). Thus, we have: \[ 9^{4} \times 9^{-3} = 9^{4-3} = 9^{1} \] Calculating \( 9^{1} \): \[ 9^{1} = 9 \] So, the value of \( 9^{4} \times \frac{1}{9^{3}} \) is **9**. ### Final Answers: - (a) \( 3^{5} \times 3^{5} = 59049 \) - (b) \( 9^{4} \times \frac{1}{9^{3}} = 9 \)