Chapter R, Problem 1T

(a)

To determine

To simplify: The expression ${\left(-3\right)}^4\cdot {\left(-3\right)}^5$.

Answer to Problem 1T

The expression ${\left(-3\right)}^4\cdot {\left(-3\right)}^5$ is simplifies as $\underset{\_}{{\left(-3\right)}^9}$.

Explanation of Solution

Given that, the expression is ${\left(-3\right)}^4\cdot {\left(-3\right)}^5$.

Simplify the expression as,

$\begin{array}{c}{\left(-3\right)}^4\cdot {\left(-3\right)}^5={\left(-3\right)}^{4+5}\left(\because \text{add the exponents}\right)\\ ={\left(-3\right)}^9\end{array}$

Therefore, the expression ${\left(-3\right)}^4\cdot {\left(-3\right)}^5$ is simplifies as $\underset{\_}{{\left(-3\right)}^9}$.

(b)

To determine

To simplify: The expression ${\left(2x^{3}y\right)}^2$.

Answer to Problem 1T

The expression ${\left(2x^{3}y\right)}^2$ is simplifies as $\underset{\_}{4x^6{y}^2}$.

Explanation of Solution

Given that, the expression is ${\left(2x^{3}y\right)}^2$.

Simplify the expression as,

$\begin{array}{c}{\left(2x^{3}y\right)}^2=\left(2^2{\left(x^3\right)}^2{y}^2\right)\\ =4x^6{y}^2\left(\because \text{add the exponents}\right)\end{array}$

Therefore, the expression ${\left(2x^{3}y\right)}^2$ is simplifies as $\underset{\_}{4x^6{y}^2}$.

(c)

To determine

To simplify: The expression ${\left(-5z\right)}^0$.

Answer to Problem 1T

The expression ${\left(-5z\right)}^0$ is simplifies as $\underset{\_}{1}$.

Explanation of Solution

Given that, the expression is ${\left(-5z\right)}^0$.

Simplify the expression as,

$\begin{array}{c}{\left(-5z\right)}^0={\left(-5\right)}^0{z}^0\\ =1\left(1\right)\\ =1\end{array}$

Therefore, the expression ${\left(-5z\right)}^0$ is simplifies as $\underset{\_}{1}$.

(d)

To determine

To simplify: The expression ${\left(-\frac{4}{5}\right)}^2$.

Answer to Problem 1T

The expression ${\left(-\frac{4}{5}\right)}^2$ is simplifies as $\underset{\_}{\frac{4^2}{5^2}}$.

Explanation of Solution

Given that, the expression is ${\left(-\frac{4}{5}\right)}^2$.

Simplify the expression as,

$\begin{array}{c}{\left(-\frac{4}{5}\right)}^2={\left(-1\right)}^2\left(\frac{4^2}{5^2}\right)\\ =1\left(\frac{4^2}{5^2}\right)\\ =\frac{4^2}{5^2}\end{array}$

Therefore, the expression ${\left(-\frac{4}{5}\right)}^2$ is simplifies as $\underset{\_}{\frac{4^2}{5^2}}$.

(e)

To determine

To simplify: The expression $-{\left(\frac{m^2}{p}\right)}^3$.

Answer to Problem 1T

The expression $-{\left(\frac{m^2}{p}\right)}^3$ is simplifies as $\underset{\_}{-\frac{m^6}{p^3}}$.

Explanation of Solution

Given that, the expression is $-{\left(\frac{m^2}{p}\right)}^3$.

Simplify the expression as,

$\begin{array}{c}-{\left(\frac{m^2}{p}\right)}^3=-\frac{{\left(m^2\right)}^3}{{\left(p\right)}^3}\left(\because {\left(a^m\right)}^n=a^{mn}\right)\\ =-\frac{m^6}{p^3}\end{array}$

Therefore, the expression $-{\left(\frac{m^2}{p}\right)}^3$ is simplifies as $\underset{\_}{-\frac{m^6}{p^3}}$.