Question

Which expression simplified would leave you with a positive exponent when simplified in exponent form? A. -2 (-3)^2 B.3^-3+3^-4 C. 3^2 (3^-5) D. 3-11/3-7

Answer 1

To determine which expression simplifies to a positive exponent, let's simplify each option one by one.

A. \(-2 (-3)^2\)
- Calculate \((-3)^2 = 9\)
- Expression becomes \(-2 \cdot 9 = -18\), which doesn't have any exponent form.

B. \(3^{-3} + 3^{-4}\)
- Combine the terms. The least power is \(3^{-4}\):
\[
3^{-3} + 3^{-4} = 3^{-4}(3^1 + 1) = 3^{-4}(3 + 1) = 3^{-4} \cdot 4
\]
- The simplified expression is \(4 \cdot 3^{-4}\), which still has a negative exponent.

C. \(3^2 (3^{-5})\)
- Combine the exponents:
\[
3^2 \cdot 3^{-5} = 3^{2 + (-5)} = 3^{-3}
\]
- This has a negative exponent.

D. \(\frac{3^{-11}}{3^{-7}}\)
- Subtract the exponents in division:
\[
3^{-11 - (-7)} = 3^{-11 + 7} = 3^{-4}
\]
- This also has a negative exponent.

Now, let's summarize:
- A leaves no exponent form.
- B simplifies to a negative exponent.
- C simplifies to a negative exponent.
- D simplifies to a negative exponent.

None of the provided options \(A\), \(B\), \(C\), or \(D\) simplify to a positive exponent.

Given the mathematical operations, none of these expressions will yield a positive exponent when simplified. If strictly looking for an option that yields a positive exponent, none suffice in this context.