Chapter R.8, Problem 1AYP

To determine

To fill: The expression “${\left(-3\right)}^2=$ _____; $-3^2=$ _____”.

Answer to Problem 1AYP

Solution:

${\left(-3\right)}^2=9$; $-3^2=-9$

Explanation of Solution

Given:

${\left(-3\right)}^2$;

$-3^2$

Formula used:

If $a$ is a real number and $n$ is a positive integer, then the symbol $a^n$ represents the product of $n$ factors of $a$. That is,

$a^n=a\cdot a\cdot a\dots a\to n$ factors.

Calculation:

The given expressions are ${\left(-3\right)}^2$ and $-3^2$.

Let us consider ${\left(-3\right)}^2$.

Here, $a=-3$ and $n=2$. That means

${\left(-3\right)}^2=-3\cdot -3=9$

Let us consider $-3^2$.

Here, $a=3$ and $n=2$. That means

$-3^2=-\left(3\right)\cdot \left(3\right)=-9$

Thus, ${\left(-3\right)}^2=9$; $-3^2=-9$.