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Simplify. Express your answer using positive exponents. \newline2y72y⋅y8\frac{2y^7}{2y \cdot y^8}

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Simplify exponential expressions using the multiplication and division rulesright chevron icon

Full solution

Q. Simplify. Express your answer using positive exponents. \newline2y72y⋅y8\frac{2y^7}{2y \cdot y^8}
  1. Identify and simplify: Identify and simplify the expression by separating coefficients and variables. 2y72y⋅y8=2y72⋅y1⋅y8\frac{2y^7}{2y \cdot y^8} = \frac{2y^7}{2 \cdot y^1 \cdot y^8}
  2. Combine y terms: Combine the y terms in the denominator.\newline2⋅y1⋅y8=2⋅y(1+8)=2⋅y92 \cdot y^1 \cdot y^8 = 2 \cdot y^{(1+8)} = 2 \cdot y^9
  3. Rewrite with simplified denominator: Rewrite the original expression with the simplified denominator. 2y72×y9=2y72y9\frac{2y^7}{2 \times y^9} = \frac{2y^7}{2y^9}
  4. Simplify expression: Simplify the expression by canceling and subtracting exponents. \newline2y72y9=22⋅y7−9=1⋅y−2=y−2\frac{2y^7}{2y^9} = \frac{2}{2} \cdot y^{7-9} = 1 \cdot y^{-2} = y^{-2}

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