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Simplify. Express your answer using positive exponents. \newline7m27m9⋅m\frac{7m^2}{7m^9 \cdot m}

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Multiply and divide powers: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline7m27m9⋅m\frac{7m^2}{7m^9 \cdot m}
  1. Simplify Inside Parentheses: Simplify the expression inside the parentheses by multiplying the terms with the same base. \newline7m27m9⋅m\frac{7m^2}{7m^9 \cdot m} can be simplified by multiplying 7m97m^9 and mm together. Since they have the same base, we add the exponents.\newline7m9⋅m=7m9+1=7m107m^9 \cdot m = 7m^{9+1} = 7m^{10}
  2. Rewrite with Simplified Denominator: Rewrite the original expression with the simplified denominator.\newlineNow we have 7m27m10\frac{7m^2}{7m^{10}}.
  3. Divide Terms with Same Base: Simplify the expression by dividing the terms with the same base and coefficients.\newlineWe can divide 7m27m^2 by 7m107m^{10}. When we divide powers with the same base, we subtract the exponents.\newline7m27m10=77×m2−10=1×m−8=m−8\frac{7m^2}{7m^{10}} = \frac{7}{7} \times m^{2-10} = 1 \times m^{-8} = m^{-8}
  4. Express Answer with Positive Exponents: Express the answer using positive exponents.\newlineSince we have m−8m^{-8}, we can rewrite it as 1/m81/m^8 to have a positive exponent.\newlinem−8=1/m8m^{-8} = 1/m^8

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