which property of exponents was used to generate the equivalent expression 3^(14) from 3^(5)/3^(-9)
5 answers
The property of exponents that was used to generate the equivalent expression is the quotient rule of exponents. According to the quotient rule, when dividing two exponential expressions with the same base, you subtract the exponents. In this case, the exponent of 3 in the numerator (5) is subtracted from the exponent of 3 in the denominator (-9), resulting in 14.
which property of exponents was used to generate the equivalent expression 3^(14) from 3^(5)/3^(-9)
only the power rule of exponents
only the product rule of exponents
only the property of negative exponents
the property of negative exponents and the product rule exponents
only the power rule of exponents
only the product rule of exponents
only the property of negative exponents
the property of negative exponents and the product rule exponents
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).
First, the property of negative exponents was used to convert 3^(-9) in the denominator to its reciprocal, which is 1/3^9. This can be done by changing the sign of the exponent and moving the base to the numerator.
Next, the product rule of exponents was applied. According to the product rule, when multiplying two exponential expressions with the same base, you add the exponents. In this case, since we have 3^(5) in the numerator and 1/3^9 (or 3^(-9) turned into reciprocal) in the denominator, the exponents 5 and -9 are added to result in 5 + (-9) = -4.
Therefore, the final equivalent expression is 3^(14), which is derived from 3^(5)/3^(-9) using the property of negative exponents and the product rule of exponents.
First, the property of negative exponents was used to convert 3^(-9) in the denominator to its reciprocal, which is 1/3^9. This can be done by changing the sign of the exponent and moving the base to the numerator.
Next, the product rule of exponents was applied. According to the product rule, when multiplying two exponential expressions with the same base, you add the exponents. In this case, since we have 3^(5) in the numerator and 1/3^9 (or 3^(-9) turned into reciprocal) in the denominator, the exponents 5 and -9 are added to result in 5 + (-9) = -4.
Therefore, the final equivalent expression is 3^(14), which is derived from 3^(5)/3^(-9) using the property of negative exponents and the product rule of exponents.
is this right?
I apologize if my previous response was unclear or if it did not fully address your question.
To generate the equivalent expression 3^(14) from 3^(5)/3^(-9), we can simplify using the product rule and the property of negative exponents.
First, let's rewrite the expression using the product rule of exponents: 3^(5)/3^(-9) = 3^(5) * (1/3^(-9)).
Next, we can apply the property of negative exponents. A negative exponent indicates that the base is in the denominator, so we can rewrite 1/3^(-9) as 3^(9) in the denominator: 3^(5) * (3^(9)).
Now, we can use the product rule of exponents. When multiplying two exponential expressions with the same base, we add the exponents. In this case, 3^(5) * 3^(9) = 3^(5+9) = 3^(14).
Therefore, the equivalent expression is indeed 3^(14), and it was generated using the product rule of exponents and the property of negative exponents.
To generate the equivalent expression 3^(14) from 3^(5)/3^(-9), we can simplify using the product rule and the property of negative exponents.
First, let's rewrite the expression using the product rule of exponents: 3^(5)/3^(-9) = 3^(5) * (1/3^(-9)).
Next, we can apply the property of negative exponents. A negative exponent indicates that the base is in the denominator, so we can rewrite 1/3^(-9) as 3^(9) in the denominator: 3^(5) * (3^(9)).
Now, we can use the product rule of exponents. When multiplying two exponential expressions with the same base, we add the exponents. In this case, 3^(5) * 3^(9) = 3^(5+9) = 3^(14).
Therefore, the equivalent expression is indeed 3^(14), and it was generated using the product rule of exponents and the property of negative exponents.