Answer :
We start with the equation
[tex]$$
1.25 \times 10^{-12} = k \times \left(4 \times 10^{-20}\right).
$$[/tex]
Our goal is to solve for [tex]$k$[/tex]. To do this, we need to isolate [tex]$k$[/tex] on one side of the equation.
1. Divide both sides of the equation by [tex]$4 \times 10^{-20}$[/tex]:
[tex]$$
k = \frac{1.25 \times 10^{-12}}{4 \times 10^{-20}}.
$$[/tex]
2. Separate the numerical coefficients and the powers of [tex]$10$[/tex]:
[tex]$$
k = \frac{1.25}{4} \times \frac{10^{-12}}{10^{-20}}.
$$[/tex]
3. Simplify the numerical coefficient:
[tex]$$
\frac{1.25}{4} = 0.3125.
$$[/tex]
4. Simplify the powers of [tex]$10$[/tex] by subtracting the exponents:
[tex]$$
\frac{10^{-12}}{10^{-20}} = 10^{-12 - (-20)} = 10^{8}.
$$[/tex]
5. Combine the results:
[tex]$$
k = 0.3125 \times 10^{8}.
$$[/tex]
6. Express the answer in standard form. To do this, write [tex]$0.3125 \times 10^{8}$[/tex] as a number between 1 and 10 multiplied by a power of [tex]$10$[/tex]. Multiply [tex]$0.3125$[/tex] by [tex]$10$[/tex] and reduce the exponent by [tex]$1$[/tex]:
[tex]$$
0.3125 \times 10^{8} = 3.125 \times 10^{7}.
$$[/tex]
Thus, the value of [tex]$k$[/tex] in standard form is
[tex]$$
k = 3.125 \times 10^{7}.
$$[/tex]
[tex]$$
1.25 \times 10^{-12} = k \times \left(4 \times 10^{-20}\right).
$$[/tex]
Our goal is to solve for [tex]$k$[/tex]. To do this, we need to isolate [tex]$k$[/tex] on one side of the equation.
1. Divide both sides of the equation by [tex]$4 \times 10^{-20}$[/tex]:
[tex]$$
k = \frac{1.25 \times 10^{-12}}{4 \times 10^{-20}}.
$$[/tex]
2. Separate the numerical coefficients and the powers of [tex]$10$[/tex]:
[tex]$$
k = \frac{1.25}{4} \times \frac{10^{-12}}{10^{-20}}.
$$[/tex]
3. Simplify the numerical coefficient:
[tex]$$
\frac{1.25}{4} = 0.3125.
$$[/tex]
4. Simplify the powers of [tex]$10$[/tex] by subtracting the exponents:
[tex]$$
\frac{10^{-12}}{10^{-20}} = 10^{-12 - (-20)} = 10^{8}.
$$[/tex]
5. Combine the results:
[tex]$$
k = 0.3125 \times 10^{8}.
$$[/tex]
6. Express the answer in standard form. To do this, write [tex]$0.3125 \times 10^{8}$[/tex] as a number between 1 and 10 multiplied by a power of [tex]$10$[/tex]. Multiply [tex]$0.3125$[/tex] by [tex]$10$[/tex] and reduce the exponent by [tex]$1$[/tex]:
[tex]$$
0.3125 \times 10^{8} = 3.125 \times 10^{7}.
$$[/tex]
Thus, the value of [tex]$k$[/tex] in standard form is
[tex]$$
k = 3.125 \times 10^{7}.
$$[/tex]
