Answer :
Let's look at each question one by one and solve them step-by-step.
### Question 1
Find the multiplicative inverse for the given expression. The expression is [tex]\(7^{-2}\)[/tex]:
- By definition, the multiplicative inverse of [tex]\(x\)[/tex] is [tex]\(\frac{1}{x}\)[/tex].
- Therefore, the multiplicative inverse of [tex]\(7^{-2}\)[/tex] is [tex]\(\frac{1}{7^{-2}}\)[/tex].
Recall that [tex]\(7^{-2} = \frac{1}{7^2}\)[/tex], so:
[tex]\[\frac{1}{7^{-2}} = \frac{1}{\left(\frac{1}{7^2}\right)} = 7^2\][/tex]
The correct option is:
(a) [tex]\(7^2\)[/tex]
### Question 2
[tex]\(2^2 \times 2^3 \times 2^4\)[/tex] can be expressed as:
- Use the property of exponents: [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
- Thus, [tex]\(2^2 \times 2^3 \times 2^4 = 2^{2+3+4} = 2^9\)[/tex].
The correct option is:
(c) [tex]\(2^9\)[/tex]
### Question 3
[tex]\((-1)^{20}=\)[/tex]:
- An even power of [tex]\(-1\)[/tex] is always 1 because [tex]\((-1)^n\)[/tex] is 1 when [tex]\(n\)[/tex] is even and [tex]\(-1\)[/tex] when [tex]\(n\)[/tex] is odd.
- Since 20 is even, [tex]\((-1)^{20} = 1\)[/tex].
The correct option is:
(b) 1
### Question 4
[tex]\(3^2 \times 3^{-4} \times 3^5\)[/tex] is equal to:
- Use the property of exponents: [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
- Thus, [tex]\(3^2 \times 3^{-4} \times 3^5 = 3^{2-4+5} = 3^3\)[/tex].
The correct option is:
(c) [tex]\(3^3\)[/tex]
### Question 5
149600000000 is equal to:
- Put the number into scientific notation: move the decimal 11 places to the left.
- Thus, [tex]\(149600000000 = 1.496 \times 10^{11}\)[/tex].
The correct option is:
(a) [tex]\(1.496 \times 10^{11}\)[/tex]
### Question 6
0.00001275 is equal to:
- Put the number into scientific notation: move the decimal 5 places to the right.
- Thus, [tex]\(0.00001275 = 1.275 \times 10^{-5}\)[/tex].
The correct option is:
(a) [tex]\(1.275 \times 10^{-5}\)[/tex]
Here's a summary of the correct options:
1. (a) [tex]\(7^2\)[/tex]
2. (c) [tex]\(2^9\)[/tex]
3. (b) 1
4. (c) [tex]\(3^3\)[/tex]
5. (a) [tex]\(1.496 \times 10^{11}\)[/tex]
6. (a) [tex]\(1.275 \times 10^{-5}\)[/tex]
### Question 1
Find the multiplicative inverse for the given expression. The expression is [tex]\(7^{-2}\)[/tex]:
- By definition, the multiplicative inverse of [tex]\(x\)[/tex] is [tex]\(\frac{1}{x}\)[/tex].
- Therefore, the multiplicative inverse of [tex]\(7^{-2}\)[/tex] is [tex]\(\frac{1}{7^{-2}}\)[/tex].
Recall that [tex]\(7^{-2} = \frac{1}{7^2}\)[/tex], so:
[tex]\[\frac{1}{7^{-2}} = \frac{1}{\left(\frac{1}{7^2}\right)} = 7^2\][/tex]
The correct option is:
(a) [tex]\(7^2\)[/tex]
### Question 2
[tex]\(2^2 \times 2^3 \times 2^4\)[/tex] can be expressed as:
- Use the property of exponents: [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
- Thus, [tex]\(2^2 \times 2^3 \times 2^4 = 2^{2+3+4} = 2^9\)[/tex].
The correct option is:
(c) [tex]\(2^9\)[/tex]
### Question 3
[tex]\((-1)^{20}=\)[/tex]:
- An even power of [tex]\(-1\)[/tex] is always 1 because [tex]\((-1)^n\)[/tex] is 1 when [tex]\(n\)[/tex] is even and [tex]\(-1\)[/tex] when [tex]\(n\)[/tex] is odd.
- Since 20 is even, [tex]\((-1)^{20} = 1\)[/tex].
The correct option is:
(b) 1
### Question 4
[tex]\(3^2 \times 3^{-4} \times 3^5\)[/tex] is equal to:
- Use the property of exponents: [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
- Thus, [tex]\(3^2 \times 3^{-4} \times 3^5 = 3^{2-4+5} = 3^3\)[/tex].
The correct option is:
(c) [tex]\(3^3\)[/tex]
### Question 5
149600000000 is equal to:
- Put the number into scientific notation: move the decimal 11 places to the left.
- Thus, [tex]\(149600000000 = 1.496 \times 10^{11}\)[/tex].
The correct option is:
(a) [tex]\(1.496 \times 10^{11}\)[/tex]
### Question 6
0.00001275 is equal to:
- Put the number into scientific notation: move the decimal 5 places to the right.
- Thus, [tex]\(0.00001275 = 1.275 \times 10^{-5}\)[/tex].
The correct option is:
(a) [tex]\(1.275 \times 10^{-5}\)[/tex]
Here's a summary of the correct options:
1. (a) [tex]\(7^2\)[/tex]
2. (c) [tex]\(2^9\)[/tex]
3. (b) 1
4. (c) [tex]\(3^3\)[/tex]
5. (a) [tex]\(1.496 \times 10^{11}\)[/tex]
6. (a) [tex]\(1.275 \times 10^{-5}\)[/tex]
