Certainly! Let's solve each part step-by-step:
### Part b:
Work out
[tex]\[
(10 - 3 \times 2)^2
\][/tex]
1. Step 1: First, perform the multiplication inside the parentheses:
[tex]\[
3 \times 2 = 6
\][/tex]
2. Step 2: Substitute this value back into the expression:
[tex]\[
10 - 6
\][/tex]
3. Step 3: Perform the subtraction:
[tex]\[
10 - 6 = 4
\][/tex]
4. Step 4: Now, square the result:
[tex]\[
4^2 = 16
\][/tex]
So, the result for part b is:
[tex]\[
(10 - 3 \times 2)^2 = 16
\][/tex]
### Part c:
Find the value of the power \( a \) if
[tex]\[
5^a = \frac{1}{125}
\][/tex]
1. Step 1: Recognize that \( \frac{1}{125} \) can be written as \( 125^{-1} \).
2. Step 2: Recall that \( 125 \) is \( 5^3 \), so we have:
[tex]\[
\frac{1}{125} = \frac{1}{5^3} = 5^{-3}
\][/tex]
3. Step 3: Hence, from the equation \( 5^a = 5^{-3} \), we can equate the exponents:
[tex]\[
a = -3
\][/tex]
So, the value of the power \( a \) is:
[tex]\[
a = -3
\][/tex]
Thus, the complete solution is:
Part b:
[tex]\[
(10 - 3 \times 2)^2 = 16
\][/tex]
Part c:
[tex]\[
a = -3 \text{ for } 5^a = \frac{1}{125}
\][/tex]
