Which property of exponents was used to generate the equivalent expression 314 from 353−9?(1 point)
Responses
the Property of Negative Exponents and the Product Rule of Exponents
the Property of Negative Exponents and the Product Rule of Exponents
only the Product Rule of Exponents
only the Product Rule of Exponents
only the Property of Negative Exponents
only the Property of Negative Exponents
only the Power Rule of Exponents
only the Property of Negative Exponents
The property of Negative Exponents and the Product Rule of Exponents were used to generate the equivalent expression 314 from 353−9.
The property of negative exponents and the product rule of exponents were used to generate the equivalent expression 314 from 353−9.
To understand how these properties were used, let's break it down step by step.
First, we start with the expression 353−9. The negative exponent property states that any nonzero number raised to a negative exponent is equal to its reciprocal raised to the positive exponent. In this case, we have 3−9, so we can rewrite it as 1/3^9.
Next, we apply the product rule of exponents, which states that when multiplying two expressions with the same base, we can add the exponents. In this case, we have 1/3^9 multiplied by 3^4. The base is 3, so we can add the exponents 9 and 4 to get a new exponent of 9 + 4 = 13.
Finally, simplifying the expression, we end up with 1/3^9 * 3^4. Since we have the same base of 3, we can combine this into a single expression 3^(4-9) = 3^(-5) = 1/3^5.
So, the expression 314 is equivalent to 353−9, and the property of negative exponents and the product rule of exponents were used to arrive at this equivalent expression. Therefore, the correct answer is "the Property of Negative Exponents and the Product Rule of Exponents."