Algebra 1 R. 11 Simplify exponential expressions using exponent rules LNK Simplify. Express your answer using positive exponents.

Sure, I'd be happy to help you simplify an exponential expression using exponent rules! To provide the most accurate assistance, could you please share the specific expression you'd like to simplify? In the meantime, here's a quick overview of some essential exponent rules that might be useful: 1. **Product of Powers Rule**: \[ a^m \times a^n = a^{m+n} \] *When multiplying like bases, you add the exponents.* 2. **Quotient of Powers Rule**: \[ \frac{a^m}{a^n} = a^{m-n} \] *When dividing like bases, you subtract the exponents.* 3. **Power of a Power Rule**: \[ (a^m)^n = a^{m \times n} \] *When raising a power to another power, you multiply the exponents.* 4. **Power of a Product Rule**: \[ (ab)^n = a^n \times b^n \] *When raising a product to a power, you raise each factor to that power.* 5. **Negative Exponent Rule**: \[ a^{-n} = \frac{1}{a^n} \] *A negative exponent indicates the reciprocal of the base raised to the positive exponent.* 6. **Zero Exponent Rule**: \[ a^0 = 1 \quad (\text{for } a \neq 0) \] *Any non-zero base raised to the zero power is 1.* ### **Example Problem** Let's go through an example to illustrate how to apply these rules: **Simplify the expression and ensure all exponents are positive:** \[ \frac{2x^{-3} \times y^4}{4x^2y^{-1}} \] **Step 1: Simplify the coefficients** \[ \frac{2}{4} = \frac{1}{2} \] **Step 2: Apply the Quotient of Powers Rule to the variables** For \( x \): \[ \frac{x^{-3}}{x^2} = x^{-3-2} = x^{-5} \] For \( y \): \[ \frac{y^4}{y^{-1}} = y^{4 - (-1)} = y^{5} \] **Step 3: Combine the simplified parts** \[ \frac{1}{2} \times x^{-5} \times y^5 = \frac{y^5}{2x^5} \] **Final Answer:** \[ \frac{y^5}{2x^5} \] All exponents are now positive. --- Feel free to provide the specific expression you're working on, and I can guide you through the simplification process step by step!