Sure! Let's break down and solve each of these expressions step by step:
### Part c:
We need to simplify the expression:
[tex]\[ \frac{6.7 \times 10^{-11} \times 2.5 \times 10^{20} \times 3.6 \times 10^{15}}{(3.35 \times 10^6)^2} \][/tex]
1. Calculate the numerator:
[tex]\[
6.7 \times 10^{-11} \times 2.5 \times 10^{20} \times 3.6 \times 10^{15}
\][/tex]
- Multiplying the coefficients: [tex]\( 6.7 \times 2.5 \times 3.6 \)[/tex]
- Combining the powers of 10: [tex]\( 10^{-11} \times 10^{20} \times 10^{15} \)[/tex]
2. Calculate the denominator:
[tex]\[
(3.35 \times 10^6)^2
\][/tex]
- Squaring the coefficient: [tex]\( 3.35^2 \)[/tex]
- Squaring the power of 10: [tex]\( (10^6)^2 = 10^{12} \)[/tex]
3. Divide the numerator by the denominator:
With the provided numerical result:
[tex]\[
\frac{6.7 \times 10^{-11} \times 2.5 \times 10^{20} \times 3.6 \times 10^{15}}{(3.35 \times 10^6)^2} \approx 5373134328358.208
\][/tex]
### Part e:
We need to simplify the expression:
[tex]\[ \frac{3.2 \times 10^3 + 4.8 \times 10^4}{1.6 \times 10^2} \][/tex]
1. Simplify the numerator:
[tex]\[
3.2 \times 10^3 + 4.8 \times 10^4
\][/tex]
- Recognize that [tex]\( 3.2 \times 10^3 \)[/tex] is [tex]\( 3200 \)[/tex]
- Recognize that [tex]\( 4.8 \times 10^4 \)[/tex] is [tex]\( 48000 \)[/tex]
- Adding them up: [tex]\( 3200 + 48000 = 51200 \)[/tex]
2. Simplify the denominator:
[tex]\[
1.6 \times 10^2
\][/tex]
- Recognize that [tex]\( 1.6 \times 10^2 \)[/tex] is [tex]\( 160 \)[/tex]
3. Divide the numerator by the denominator:
With the provided numerical result:
[tex]\[
\frac{3.2 \times 10^3 + 4.8 \times 10^4}{1.6 \times 10^2} = \frac{51200}{160} \approx 320.0
\][/tex]
So, the detailed solutions for the given expressions are:
- For part c: [tex]\(\approx 5373134328358.208\)[/tex]
- For part e: [tex]\(\approx 320.0\)[/tex]
