(b) y-1 Write the reciprocal of y -1 and change the sign of the exponent. 1 y (c) (-2)-3 2 x Because of the parentheses, the base is -2. Write the reciprocal of (-2)-3 and change the exponent from -3 to 3. (-2) (-2)3 = -8. 16 x (d) 5-2 - 10-2 = Write the reciprocal of 5-2 and 10-2 and change the sign of each exponent. Evalute: 52 = 25 and 102 = 100. 27 81 X 1 Build 1/25 to have a denominator of 100 so that the fractions can be subtracted: 1/25 = 1/25 · 4/4 = 4/100 %3D 100 100 2 X 100
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
I need help with b, c and d.
![### Expressing Negative Exponents with Positive Exponents
In mathematics, expressing negative exponents in terms of positive exponents can simplify many problems, following the negative exponent rule. This rule allows us to convert an exponential expression with a negative exponent into an equivalent expression with a positive exponent.
Consider the following examples and their simplifications:
#### Example (a) \( 3^{-2} \)
\[
\begin{aligned}
&= \frac{1}{3^2} &\quad \text{Write the reciprocal of \(3^{-2}\) and change the sign of the exponent.} \\
&= \frac{1}{9} &\quad 3^2 = 9. \\
\end{aligned}
\]
#### Example (b) \( y^{-1} \)
\[
\begin{aligned}
&= \frac{1}{y^1} &\quad \text{Write the reciprocal of \( y^{-1} \) and change the sign of the exponent.} \\
&= \frac{1}{y} \\
\end{aligned}
\]
#### Example (c) \( (-2)^{-3} \)
\[
\begin{aligned}
&= \frac{1}{(-2)^3} &\quad \text{Because of the parentheses, the base is \(-2\). Write the reciprocal of \((-2)^{-3}\) and change the exponent from \(-3\) to \(3\).} \\
&= \frac{1}{-8} &\quad (-2)^3 = -8. \\
\end{aligned}
\]
#### Example (d) \( 5^{-2} - 10^{-2} \)
\[
\begin{aligned}
&= \frac{1}{5^2} - \frac{1}{10^2} &\quad \text{Write the reciprocal of \(5^{-2}\) and \(10^{-2}\) and change the sign of each exponent.} \\
&= \frac{1}{25} - \frac{1}{100} &\quad \text{Evaluate: } 5^2 = 25 \text{ and } 10^2 = 100. \\
&= \frac{4}{100} - \frac{1}{100} &\quad \text{Build \( \frac{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46673039-9c26-4fb7-977e-77e5eaa45b18%2Fb8daba8b-8284-4afb-bb8a-f61563d79f84%2Fmjnybk8_processed.png&w=3840&q=75)
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