Questions: Objective A: Simplify Expressions Containing Negative Exponents YOUR TURN # 3 Simplify the expression. Write the result using positive exponents only. Assume that all bases are not equal to 0. y^-2/y y^-2/y=

Solution Steps

To simplify the expression \(\frac{y^{-2}}{y}\) and write the result using positive exponents only, we can use the properties of exponents. Specifically, we can use the rule that states \(a^{-m} = \frac{1}{a^m}\) and the rule for dividing exponents with the same base, which is \(a^m / a^n = a^{m-n}\).

1. Apply the rule for dividing exponents with the same base: \(\frac{y^{-2}}{y} = y^{-2-1}\).
2. Simplify the exponent: \(y^{-3}\).
3. Convert the negative exponent to a positive exponent: \(y^{-3} = \frac{1}{y^3}\).

We start with the expression

\[ \frac{y^{-2}}{y} \]

Using the property of exponents that states

\[ \frac{a^m}{a^n} = a^{m-n} \]

we can rewrite the expression as

\[ y^{-2-1} = y^{-3} \]

Next, we convert the negative exponent to a positive exponent using the rule

\[ a^{-m} = \frac{1}{a^m} \]

Thus, we have

\[ y^{-3} = \frac{1}{y^3} \]

Final Answer