Question - Simplifying Fractional Exponents
Solution:
To simplify the given expression $$ \frac{2x^7y}{8x^9y^2} $$, you'll need to divide the numerator by the denominator for each variable and the coefficients.Step 1 - Simplify the coefficients:Divide the coefficients $$2$$ and $$8$$:\[ \frac{2}{8} = \frac{1}{4} \]Step 2 - Simplify the x terms:When you divide terms with the same base, you subtract the exponents (according to the law of exponents):\[ x^7 / x^9 = x^{7-9} = x^{-2} \]Since a negative exponent indicates that you should take the reciprocal of the base raised to the positive exponent, $$ x^{-2} $$ can be rewritten as $$ 1/x^2 $$ if the expression is required to have only positive exponents.Step 3 - Simplify the y terms:For the y terms:\[ y / y^2 = y^{1-2} = y^{-1} \]Again, for positive exponents, $$ y^{-1} $$ would be $$ 1/y $$.Combining these results, the simplified expression is:\[ \frac{1}{4} \cdot \frac{1}{x^2} \cdot \frac{1}{y} \]Or more simply:\[ \frac{1}{4x^2y} \]This is your final simplified expression.
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