QQuestionMathematics
QuestionMathematics
Rewrite $8 \sqrt{8}$ in the form $8^{k}$. Find the value of $k$.
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Answer
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Step 1:I'll solve this step by step using the guidelines you specified:
Step 2:: Simplify the radical \sqrt{8}
• $$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2}
• \sqrt{8} = 2\sqrt{2}
Step 3:: Rewrite the original expression
• $$8 \sqrt{8} = 8 \times 2\sqrt{2}
• 8 \sqrt{8} = 16\sqrt{2}
Step 4:: Rewrite 16\sqrt{2} as a power of 8
• $$16\sqrt{2} = 8 \times 2^{3/2}
• 16 = 8 \times 2
Step 5:: Identify the exponent
• $$k = 1 + \frac{3}{2} = \frac{5}{2}
• 8^{k} = 8 \times 2^{3 / 2}
Final Answer
k = \frac{5}{2}
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