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$y^{9}\div y^{\frac{1}{2}}=$

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Add, subtract, multiply, or divide two fractions

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Q.

y^{9}\div y^{\frac{1}{2}}=

Apply Quotient Rule: Apply the quotient rule for exponents which states that when dividing like bases, you subtract the exponents. $\newline$ $y^{9} \div y^{\frac{1}{2}} = y^{9 - \frac{1}{2}}$
Convert Exponent to Fraction: Convert the exponent $9$ to a fraction to have a common denominator with $\frac{1}{2}$ . The number $9$ is equivalent to $\frac{18}{2}$ when expressed as a fraction with a denominator of $2$ . $\newline$ $y^{\left(\frac{18}{2} - \frac{1}{2}\right)} = y^{\frac{17}{2}}$
Perform Subtraction: Perform the subtraction of the fractions in the exponent. $\newline$ $\frac{18}{2} - \frac{1}{2} = \frac{17}{2}$ $\newline$ So, $y^{9} \div y^{\frac{1}{2}} = y^{\frac{17}{2}}$

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