Question

Which expression simplified would leave you with a positive exponent when simplified in exponent form?(1 point)
Responses

−2(−3)2
negative 2 times negative 3 squared

3−3+3−4
3 to the negative 3 power plus 3 to the negative 4 power

32(3−5)
3 squared times open paren 3 to the negative 5 power close paren

3−113−7
the fraction with numerator 3 to the negative 11 power and denominator 3 to the negative 7 power

Answer 1

To determine which expression simplifies to a positive exponent, let's analyze each option:

1. **−2(−3)²**
- This simplifies to:
\(-2 \times 9 = -18\)
- This expression is a constant (negative) and does not involve exponents in the simplified form.

2. **3^(-3) + 3^(-4)**
- This can be expressed as:
\(\frac{1}{3^3} + \frac{1}{3^4} = \frac{1}{27} + \frac{1}{81}\)
- The result is positive, but all terms involve negative exponents when written in exponent form.

3. **3²(3^(-5))**
- This simplifies using the property of exponents \(a^m \times a^n = a^{m+n}\):
\[3^{2 + (-5)} = 3^{-3}\]
- The result is still a negative exponent.

4. **3^(-11) / 3^(-7)**
- This simplifies using the property of exponents \(a^m / a^n = a^{m-n}\):
\[3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4}\]
- The resulting exponent is negative.

From the analysis above, none of the expressions result in a positive exponent after simplification. However, if "which expression simplifies to a positive exponent" implies that the reference to positive exponent ultimately leads to a simplified expression considered, then technically, all of these responses lead to outcomes with non-negative or non-exponent context.

If adjusted clearly under assumptions, the only one that consistently keeps a framework on the output could be treated as option 2 with the sum of fractions resulting ultimately indicating a positive value. However, formally and literally none yield positive exponent outcomes in final exponent terms.