Question

Evaluate the following expressions.
a.
10 Superscript 5 Baseline times 10 Superscript 8
b.
10 Superscript 7 Baseline times 10 Superscript negative 5
c.
StartFraction 10 Superscript 8 Over 10 Superscript 4 EndFraction
d.
StartFraction 10 Superscript 8 Over 10 Superscript negative 2 EndFraction
Question content area bottom
Part 1
a. 10 Superscript 5 Baseline times 10 Superscript 8equals
  
enter your response here ​(Simplify your answer. Type your answer using exponential​ notation.)

Answer 1

To evaluate the expressions provided, we will use the laws of exponents. Here’s how to address each part:

### Part a
The expression is:
\[
10^{5} \times 10^{8}
\]
Using the property of exponents that states \(a^m \times a^n = a^{m+n}\):
\[
10^{5} \times 10^{8} = 10^{5 + 8} = 10^{13}
\]

**Answer for part a**: \(10^{13}\)

---

### Part b
The expression is:
\[
10^{7} \times 10^{-5}
\]
Again using the property of exponents:
\[
10^{7} \times 10^{-5} = 10^{7 + (-5)} = 10^{2}
\]

**Answer for part b**: \(10^{2}\)

---

### Part c
The expression is:
\[
\frac{10^{8}}{10^{4}}
\]
Using the property of exponents that states \(\frac{a^m}{a^n} = a^{m-n}\):
\[
\frac{10^{8}}{10^{4}} = 10^{8 - 4} = 10^{4}
\]

**Answer for part c**: \(10^{4}\)

---

### Part d
The expression is:
\[
\frac{10^{8}}{10^{-2}}
\]
Using the property of exponents:
\[
\frac{10^{8}}{10^{-2}} = 10^{8 - (-2)} = 10^{8 + 2} = 10^{10}
\]

**Answer for part d**: \(10^{10}\)

Hence, the answers to all parts are:
- Part a: \(10^{13}\)
- Part b: \(10^{2}\)
- Part c: \(10^{4}\)
- Part d: \(10^{10}\)