Question

which of the following is equavilant to 32^1.4
^7 square root of 32^5
^5 square root of 32^7
32^1+32^4
32+1times32^4

Answer 1

To determine which of the expressions is equivalent to \( 32^{1.4} \), we can simplify each option step by step.

1. **Option 1: \( \sqrt[7]{32^5} \)**

\[
\sqrt[7]{32^5} = (32^5)^{1/7} = 32^{5/7}
\]

2. **Option 2: \( \sqrt[5]{32^7} \)**

\[
\sqrt[5]{32^7} = (32^7)^{1/5} = 32^{7/5}
\]

3. **Option 3: \( 32^1 + 32^4 \)**

\[
32^1 + 32^4 = 32 + 32^4
\]
This does not simplify to a single exponent.

4. **Option 4: \( 32 + 1 \times 32^4 \)**

\[
32 + 1 \times 32^4 = 32 + 32^4
\]
Similar to option 3.

Now we will convert \( 1.4 \) to a fraction for easier comparison:

\[
1.4 = \frac{14}{10} = \frac{7}{5}
\]

Now, we compare the fractional exponents:

- \( 32^{1.4} = 32^{7/5} \)
- From our evaluations:
- \( \sqrt[5]{32^7} = 32^{7/5} \)

Hence, the expression that is equivalent to \( 32^{1.4} \) is:
\[
\sqrt[5]{32^7}
\]

So, the correct answer is:
\[
\boxed{\sqrt[5]{32^7}}
\]