Ce this expanded form as a power. \( \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \) Determine these values. 713 b) \( 4^{4} \) Pewrite \( 7,9 \times 10^{8} \) in decimal notation. Arrange these powers in descending order of value: \( 3^{5} ; 5^{3} ; 9^{2} ; 4^{4} ; 136^{10} ; 2^{7} \) Which is greater: \( 4^{5} \) or \( 5^{4} \) ? n the power \( 12^{5} \), which number is the exponent? Write these expanded forms as powers. \[ 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \] b) \( 6 \times 6 \times 6 \times 6 \times 6 \times 8 \times 8 \times 8 \) Express 86500000000 in scientific notation.

Calculate the value by following steps: - step0: Calculate: \(4^{4}\) - step1: Evaluate the power: \(256\) Calculate or simplify the expression \( 9^2 \). Calculate the value by following steps: - step0: Calculate: \(9^{2}\) - step1: Evaluate the power: \(81\) Calculate or simplify the expression \( 86500000000 \). Numbers by following steps: - step0: Solution: \(86500000000\) Expand the expression \( 7^6 \) Simplify the expression by following steps: - step0: : \(7^{6}\) Calculate or simplify the expression \( 3^5 \). Calculate the value by following steps: - step0: Calculate: \(3^{5}\) - step1: Evaluate the power: \(243\) Calculate or simplify the expression \( 7.9*10^8 \). Calculate the value by following steps: - step0: Calculate: \(7.9\times 10^{8}\) Calculate or simplify the expression \( 713 \). Numbers by following steps: - step0: Solution: \(713\) Calculate or simplify the expression \( 5^3 \). Calculate the value by following steps: - step0: Calculate: \(5^{3}\) - step1: Evaluate the power: \(125\) Calculate or simplify the expression \( 2^7 \). Calculate the value by following steps: - step0: Calculate: \(2^{7}\) - step1: Evaluate the power: \(128\) Calculate or simplify the expression \( 4^4 \). Calculate the value by following steps: - step0: Calculate: \(4^{4}\) - step1: Evaluate the power: \(256\) Calculate or simplify the expression \( 136^10 \). Calculate the value by following steps: - step0: Calculate: \(136^{10}\) Solve the equation \( 4^5 > 5^4 \). Check the inequality by following steps: - step0: Check the inequality is true or false: \(4^{5}>5^{4}\) - step1: Calculate: \(1024>5^{4}\) - step2: Calculate: \(1024>625\) - step3: Check the inequality: \(\textrm{true}\) Let's break down the problem step by step: 1. **Expanded Form as a Power:** - The expression \( \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \) can be written as \( 7^6 \). - The value of \( 7^6 \) is \( 117649 \). 2. **Determine Values:** - \( 713 \) is simply \( 713 \). - \( 4^4 = 256 \). 3. **Decimal Notation:** - \( 7.9 \times 10^8 \) in decimal notation is \( 790000000 \). 4. **Arrange Powers in Descending Order:** - Calculate the values: - \( 3^5 = 243 \) - \( 5^3 = 125 \) - \( 9^2 = 81 \) - \( 4^4 = 256 \) - \( 136^{10} \approx 2.164657 \times 10^{21} \) - \( 2^7 = 128 \) - Arranging these in descending order: - \( 136^{10} \) - \( 4^4 = 256 \) - \( 3^5 = 243 \) - \( 2^7 = 128 \) - \( 5^3 = 125 \) - \( 9^2 = 81 \) 5. **Comparison of Powers:** - To determine which is greater between \( 4^5 \) and \( 5^4 \): - \( 4^5 = 1024 \) - \( 5^4 = 625 \) - Therefore, \( 4^5 \) is greater than \( 5^4 \). 6. **Exponent in \( 12^5 \):** - The exponent in \( 12^5 \) is \( 5 \). 7. **Expanded Forms as Powers:** - For \( 3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 5 \): - This can be written as \( 3^4 \times 5^3 \). - For \( 6 \times 6 \times 6 \times 6 \times 6 \times 8 \times 8 \times 8 \): - This can be written as \( 6^5 \times 8^3 \). 8. **Scientific Notation:** - The number \( 86500000000 \) in scientific notation is \( 8.65 \times 10^{10} \). ### Summary of Results: - Expanded form of \( 7 \times 7 \times 7 \times 7 \times 7 \times 7 \): \( 7^6 \) (Value: \( 117649 \)) - Value of \( 713 \): \( 713 \) - Value of \( 4^4 \): \( 256 \) - Decimal notation of \( 7.9 \times 10^8 \): \( 790000000 \) - Powers in descending order: \( 136^{10}, 4^4, 3^5, 2^7, 5^3, 9^2 \) - Greater power: \( 4^5 > 5^4 \) - Exponent in \( 12^5 \): \( 5 \) - Expanded forms: \( 3^4 \times 5^3 \) and \( 6^5 \times 8^3 \) - Scientific notation of \( 86500000000 \): \( 8.65 \times 10^{10} \)