Evaluate the expression:

[tex]\frac{\left(5.2 \times 10^7\right)\left(5 \times 10^8\right)}{\left(3.2 \times 10^6\right)\left(5 \times 10^5\right)}[/tex]

Choose the correct answer:

A. [tex]1.625 \times 10^4[/tex]

B. [tex]1.625 \times 10^5[/tex]

C. [tex]8.125 \times 10^4[/tex]

D. [tex]8125 \times 10^5[/tex]

Sure! Let's solve the given expression step-by-step. We are working with scientific notation.

We want to simplify this expression:

[tex]\[
\frac{(5.2 \times 10^7) \times (5 \times 10^8)}{(3.2 \times 10^6) \times (5 \times 10^5)}
\][/tex]

### Step 1: Simplify the Numerator

First, let's focus on the numerator:

[tex]\[
(5.2 \times 10^7) \times (5 \times 10^8)
\][/tex]

Multiply the coefficients (5.2 and 5):

[tex]\[
5.2 \times 5 = 26
\][/tex]

Now add the exponents of 10:

[tex]\[
10^7 \times 10^8 = 10^{7+8} = 10^{15}
\][/tex]

So, the simplified numerator is:

[tex]\[
26 \times 10^{15}
\][/tex]

### Step 2: Simplify the Denominator

Now simplify the denominator:

[tex]\[
(3.2 \times 10^6) \times (5 \times 10^5)
\][/tex]

Multiply the coefficients (3.2 and 5):

[tex]\[
3.2 \times 5 = 16
\][/tex]

Add the exponents of 10:

[tex]\[
10^6 \times 10^5 = 10^{6+5} = 10^{11}
\][/tex]

So, the simplified denominator is:

[tex]\[
16 \times 10^{11}
\][/tex]

### Step 3: Divide the Simplified Numerator by the Simplified Denominator

Now, let's divide:

[tex]\[
\frac{26 \times 10^{15}}{16 \times 10^{11}}
\][/tex]

Divide the coefficients (26 and 16):

[tex]\[
\frac{26}{16} = 1.625
\][/tex]

Subtract the exponents of 10:

[tex]\[
10^{15} \div 10^{11} = 10^{15-11} = 10^4
\][/tex]

So, the result of the division is:

[tex]\[
1.625 \times 10^4
\][/tex]

Hence, the correct answer is:

A [tex]$ \quad 1.625 \times 10^4 $[/tex]