Which property of exponents was used to generate the equivalent expression 314
from 353−9
?(1 point)
Responses
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 Power Rule of Exponents
the Property of Negative Exponents and the Product Rule of 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 generate the equivalent expression 314 from 353−9, we need to understand the properties of exponents that were used.
In this case, two properties of exponents were used: the Property of Negative Exponents and the Product Rule of Exponents.
The Property of Negative Exponents states that any base raised to a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent. In this case, the exponent -9 was negative, so we can rewrite it as 1/35^9.
The Product Rule of Exponents states that when multiplying two exponential expressions with the same base, we can add their exponents. So in this case, we have 3^5 multiplied by 1/35^9. Using the product rule, we add the exponents 5 and -9, which gives us 3^5 + (-9) = 3^5 - 9.
Simplifying further, 3^5 is equal to 243, so the equivalent expression becomes 243 - 9 = 234.
Therefore, the Property of Negative Exponents and the Product Rule of Exponents were both used to generate the equivalent expression 314 from 353−9.