Convert the given number to decimal form by expanding in powers and by using the calculator shortcut. \( 53221_{\text {six }} \) Expand \( 53221_{\text {six }} \) in powers. \( 53221_{\text {six }}=(\square)+(\square)+(\square)+(\square)+(\square) \) (Use descending order. Do not simplify.) Convert \( 53221_{\text {six }} \) to decimal form. \( 53221_{\text {six }}=\square \) (Simplify your answer.)

To convert the number \(53221_{\text{six}}\) to decimal form, we need to expand it in powers of 6 and then simplify the expression. Given number in base 6: \(53221_{\text{six}}\) Expanding in powers of 6: \(53221_{\text{six}} = 5 \times 6^4 + 3 \times 6^3 + 2 \times 6^2 + 2 \times 6^1 + 1 \times 6^0\) Now, let's calculate the decimal form of \(53221_{\text{six}}\). Calculate the value by following steps: - step0: Calculate: \(5\times 6^{4}+3\times 6^{3}+2\times 6^{2}+2\times 6^{1}+1\times 6^{0}\) - step1: Evaluate the power: \(5\times 6^{4}+3\times 6^{3}+2\times 6^{2}+2\times 6^{1}+1\times 1\) - step2: Evaluate the power: \(5\times 6^{4}+3\times 6^{3}+2\times 6^{2}+2\times 6+1\times 1\) - step3: Multiply the terms: \(6480+3\times 6^{3}+2\times 6^{2}+2\times 6+1\times 1\) - step4: Multiply the terms: \(6480+648+2\times 6^{2}+2\times 6+1\times 1\) - step5: Multiply the terms: \(6480+648+72+2\times 6+1\times 1\) - step6: Multiply the numbers: \(6480+648+72+12+1\times 1\) - step7: Calculate: \(6480+648+72+12+1\) - step8: Add the numbers: \(7213\) The decimal form of \(53221_{\text{six}}\) is 7213.