Evaluate $$ \left(\frac{3.5^{7}}{3.5^{6}}\right)^{2} $$

Question

UpStudy AI · Accepted Answer

To evaluate the expression:

$$
\left(\frac{3.5^{7}}{3.5^{6}}\right)^{2}
$$

Let's break it down step by step.

### Step 1: Simplify the Fraction

When you have the same base with exponents in a fraction, you can subtract the exponents:

$$
\frac{a^m}{a^n} = a^{m-n}
$$

Applying this to our expression:

$$
\frac{3.5^{7}}{3.5^{6}} = 3.5^{7-6} = 3.5^{1} = 3.5
$$

### Step 2: Square the Result

Now, square the simplified result:

$$
\left(3.5\right)^{2} = 3.5 \times 3.5 = 12.25
$$

### Final Answer

$$
\left(\frac{3.5^{7}}{3.5^{6}}\right)^{2} = 12.25
$$
The value of the expression is 12.25.

Evaluate \( \left(\frac{3.5^{7}}{3.5^{6}}\right)^{2} \)