Which property of exponents was used to generate the equivalent expression 3^14 from (3 ^ 5)/(3 ^ - 9) ?
The property used to generate the equivalent expression 3^14 from (3 ^ 5)/(3 ^ -9) is the Product of Powers Property. This property states that when multiplying two powers that have the same base, you add the exponents. In this case, we have 3^5 divided by 3^-9. To convert this to an equivalent expression with the same base, we can rewrite the division as multiplication with the reciprocal of the second term. Thus, (3^5)/(3^-9) is equal to 3^5 * 3^9. Applying the Product of Powers Property, we add the exponents to get a new exponent of 14. Hence, (3^5)/(3^-9) is equivalent to 3^14.
The property of exponents that was used to generate the equivalent expression 3^14 from (3 ^ 5)/(3 ^ - 9) is the rule for dividing powers with the same base.
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answer choices :
only the property of negative exponents
the property of negative exponents and the product rule of exponents
only the power rule of negative exponents
only the product rule of exponents
Which property of exponents was used to generate the equivalent expression 3^14 from (3 ^ 5)/(3 ^ - 9) ?
only the property of negative exponents
the property of negative exponents and the product rule of exponents
only the power rule of negative exponents
only the product rule of exponents
To generate the equivalent expression 3^14 from (3 ^ 5)/(3 ^ - 9), the property of exponents that was used is the quotient rule.
The quotient rule states that when dividing two numbers with the same base, you subtract the exponents. In other words, a^m / a^n = a^(m - n).
In this case, we have (3 ^ 5)/(3 ^ - 9). According to the quotient rule, we subtract the exponents, so the expression can be rewritten as 3^(5 - (-9)). Simplifying the exponent, we have 3^14, which is the equivalent expression.
So, the property of exponents used is the quotient rule.