I need help with b, c and d. ### Expressing Negative Exponents with Positive ExponentsIn 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{

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Description: I need help with b, c and d. ### Expressing Negative Exponents with Positive ExponentsIn mathematics, expressing negative exponents in terms of positive exponents can simplify many problems, following the negative exponent rule. This rule allows us t

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(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

(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

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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{

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