Question

Review the properties of exponents. In complete sentences, explain the process necessary to simplify the exponential expression. Complete your work in the space provided. Include your explanation, the mathematical steps, and the final, simplified expression.

Simplify the expression: 2ab⁻¹ x 3a⁻³d

Answer 1

To simplify the expression 2ab⁻¹ x 3a⁻³d, multiply the coefficients, add the exponents of 'a', and keep the unique bases 'b' and 'd'. The final expression is 6a⁻²b⁻¹d, which can be written as 6bd/(a²b) without negative exponents.

Step-by-step explanation:

When simplifying the expression 2ab⁻¹ x 3a⁻³d, we need to apply the properties of exponents. The multiplication of exponential expressions allows us to multiply the coefficients (numerical parts) and add the exponents of like bases. In the case of dividing exponentials, you divide the coefficients and subtract the exponents of like bases.

To simplify the given expression:

1. Multiply the coefficients: 2 x 3 = 6.
2. Add the exponents of the base 'a': 1 + (-3) = -2.
3. Since there are no other 'b' terms in the second expression, b⁻¹ remains as it is.
4. The base 'd' only occurs in the second expression, so it simply carries over.

Combining all these steps, the final simplified expression is 6a⁻²b⁻¹d.

Remember, negative exponents indicate that the base is in the denominator. The expression 6a⁻²b⁻¹d can also be written as 6bd/(a²b) if we want to express it without negative exponents.