Sure, let's break down each multiplication problem step by step.
### 4) [tex]\(\left(5 \times 10^{-2}\right)\left(5 \times 10^{-8}\right)\)[/tex]
1. Multiply the coefficients: [tex]\(5 \times 5 = 25\)[/tex].
2. Add the exponents of 10: [tex]\(-2 + (-8) = -10\)[/tex].
So, [tex]\[\left(5 \times 10^{-2}\right)\left(5 \times 10^{-8}\right) = 25 \times 10^{-10} = 2.5 \times 10^{-9}\][/tex]
### 5) [tex]\(\left(1.2 \times 10^{-7}\right)\left(4.3 \times 10^5\right)\)[/tex]
1. Multiply the coefficients: [tex]\(1.2 \times 4.3 = 5.16\)[/tex].
2. Add the exponents of 10: [tex]\(-7 + 5 = -2\)[/tex].
So, [tex]\[\left(1.2 \times 10^{-7}\right)\left(4.3 \times 10^5\right) = 5.16 \times 10^{-2} = 0.0516\][/tex]
### 6) [tex]\(\left(2.6 \times 10^3\right)\left(3.7 \times 10^{-4}\right)\)[/tex]
1. Multiply the coefficients: [tex]\(2.6 \times 3.7 = 9.62\)[/tex].
2. Add the exponents of 10: [tex]\(3 + (-4) = -1\)[/tex].
So, [tex]\[\left(2.6 \times 10^3\right)\left(3.7 \times 10^{-4}\right) = 9.62 \times 10^{-1} = 0.962\][/tex]
Therefore, the results of the three calculations are:
1. [tex]\(2.5 \times 10^{-9}\)[/tex]
2. [tex]\(0.0516\)[/tex]
3. [tex]\(0.962\)[/tex]
These correspond to the numerical values [tex]\(2.5 \times 10^{-9}\)[/tex], [tex]\(0.0516\)[/tex], and [tex]\(0.962\)[/tex].
