Which property of exponents was used to generate the equivalent expression 3^14 from 3^5 / 3^−9?(1 point) Responses only the Property of Negative Exponents only the Property of Negative Exponents the Property of Negative Exponents and the Product Rule of Exponents the Property of Negative Exponents and the Product Rule of Exponents only the Power Rule of Exponents only the Power Rule of Exponents only the Product Rule of Exponents.
3 answers
The property of negative exponents and the product rule of exponents were used to generate the equivalent expression 3^14 from 3^5 / 3^−9.
how
To see how the property of negative exponents and the product rule of exponents were used, let's break down the original expression:
3^5 / 3^−9
The property of negative exponents states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent. So we can rewrite the expression as:
3^5 / (1 / 3^9)
Now, applying the product rule of exponents, which states that when you divide two numbers with the same base, you subtract the exponents, we have:
3^5 * 3^9 (the reciprocal is now in the numerator)
Simplifying further using the power rule of exponents, which states that when you multiply two numbers with the same base, you add the exponents, we get:
3^(5 + 9)
This simplifies to:
3^14
So, in total, we used the property of negative exponents (to convert the negative exponent to a positive exponent of the reciprocal) and the product rule of exponents (to combine the two expressions with the same base).
3^5 / 3^−9
The property of negative exponents states that any number raised to a negative exponent is equal to its reciprocal raised to the positive exponent. So we can rewrite the expression as:
3^5 / (1 / 3^9)
Now, applying the product rule of exponents, which states that when you divide two numbers with the same base, you subtract the exponents, we have:
3^5 * 3^9 (the reciprocal is now in the numerator)
Simplifying further using the power rule of exponents, which states that when you multiply two numbers with the same base, you add the exponents, we get:
3^(5 + 9)
This simplifies to:
3^14
So, in total, we used the property of negative exponents (to convert the negative exponent to a positive exponent of the reciprocal) and the product rule of exponents (to combine the two expressions with the same base).
1 answer