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Simplify. Express your answer using positive exponents.\newline8v8v8\frac{8v}{8v^8}

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Q. Simplify. Express your answer using positive exponents.\newline8v8v8\frac{8v}{8v^8}
  1. Write Expression: Write down the given expression.\newlineThe given expression is 8v8v8\frac{8v}{8v^8}. We need to simplify this expression.
  2. Simplify Coefficients: Simplify the coefficients.\newlineBoth the numerator and the denominator have the coefficient 88. We can simplify this by dividing 88 by 88, which equals 11.\newline88=1\frac{8}{8} = 1
  3. Simplify Variables: Simplify the variables using the laws of exponents.\newlineWe have vv in the numerator and v8v^8 in the denominator. According to the laws of exponents, when we divide like bases, we subtract the exponents.\newlinevv8=v18=v7\frac{v}{v^8} = v^{1-8} = v^{-7}
  4. Combine Coefficients and Variables: Combine the simplified coefficients and variables.\newlineSince the coefficient simplifies to 11, and we are left with v7v^{-7}, the expression simplifies to:\newline1×v7=v71 \times v^{-7} = v^{-7}
  5. Convert to Positive Exponents: Express the answer using positive exponents.\newlineThe question asks for the answer to be expressed using positive exponents. To convert a negative exponent to a positive exponent, we take the reciprocal of the base raised to the positive of the negative exponent.\newlinev7=1v7v^{-7} = \frac{1}{v^7}

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