Questions: Simplify. (y^3)^-3 Write your answer without using negative exponents.

Transcript text: MyHCC Aleks LTIA 1.3 https://www-awy.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNsIkr7j8P3jH-IBg Exponents and Polynomials Power of a power rule with negative exponents Simplify. \[ \left(y^{3}\right)^{-3} \] Write your answer without using negative exponents. $\square$ Explanation Check

Solution

Solution Steps

To simplify the expression $(y^{3})^{-3}$ using the power of a power rule, you multiply the exponents. Then, to eliminate the negative exponent, take the reciprocal of the base raised to the positive exponent.

Step 1: Apply the Power of a Power Rule

Using the power of a power rule, we simplify the expression $(y^{3})^{-3}$ by multiplying the exponents: \[ (y^{3})^{-3} = y^{3 \cdot (-3)} = y^{-9} \]

Step 2: Eliminate the Negative Exponent

To express the result without a negative exponent, we take the reciprocal of the base: \[ y^{-9} = \frac{1}{y^{9}} \]