Let's solve each question step-by-step.
Question 7: [tex]\(3^{-2} \times 3^{-5}\)[/tex]
To solve this, we use the property of exponents which states that [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
Given:
[tex]\[3^{-2} \times 3^{-5}\][/tex]
Using the exponent rule:
[tex]\[
3^{-2} \times 3^{-5} = 3^{-2 + (-5)} = 3^{-7}
\][/tex]
So, the correct answer is:
(a) [tex]\(3^{-7}\)[/tex]
Question 8: [tex]\(3^2 \times 4^2\)[/tex]
First, calculate each term:
[tex]\[3^2 = 3 \times 3 = 9\][/tex]
[tex]\[4^2 = 4 \times 4 = 16\][/tex]
Now, multiply the two results:
[tex]\[3^2 \times 4^2 = 9 \times 16 = 144\][/tex]
So, the correct answer is:
(c) 144
Question 9: [tex]\(100^0 + 20^0 + 5^0\)[/tex]
Recall that any non-zero number raised to the power of 0 is 1. Thus:
[tex]\[100^0 = 1\][/tex]
[tex]\[20^0 = 1\][/tex]
[tex]\[5^0 = 1\][/tex]
Add these together:
[tex]\[100^0 + 20^0 + 5^0 = 1 + 1 + 1 = 3\][/tex]
So, the correct answer is:
(d) 3
Question 10: If [tex]\((-3)^{m+1} \times (-3)^5 = (-3)^7\)[/tex], then the value of [tex]\(m\)[/tex] is:
Using the same exponent rule [tex]\(a^m \times a^n = a^{m+n}\)[/tex]:
[tex]\[
(-3)^{m+1} \times (-3)^5 = (-3)^{(m+1)+5} = (-3)^7
\][/tex]
According to the given equality:
[tex]\[
(-3)^{(m+1)+5} = (-3)^7
\][/tex]
This implies:
[tex]\[
(m+1) + 5 = 7
\][/tex]
Simplify the equation:
[tex]\[
m + 1 + 5 = 7
\][/tex]
[tex]\[
m + 6 = 7
\][/tex]
Solve for [tex]\(m\)[/tex]:
[tex]\[
m = 7 - 6
\][/tex]
[tex]\[
m = 1
\][/tex]
So, the correct answer is:
(c) 1
