Question

Select all the numbers which are positive.

• A. $(-5{)}^2$
• B. $(-7{)}^3$
• C. $9^3$
• D. $-6^8$

Answer 1

Answer: (A), (C)

$9^3$

As we know, a negative base raised to an even power always gives a positive value. A negative base raised to an odd power always gives a negative value.

For $a<0,$

• $a^n$ is positive if $n$ is even, and
• $a^n$ is negative if $n$ is odd

Now, let's elaborate all the options one-by-one:

$\bullet$ In $(-5{)}^2,$ base $(-5)$ is negative and exponent $\left(2\right)$ is even. Therefore, $(-5{)}^2$ has a positive value.

$\bullet$ In $(-7{)}^3,$ base $(-7)$ is negative and exponent $\left(3\right)$ is odd. Therefore, $(-7{)}^3$ has a negative value.

$\bullet$ A positive base raised to any power always gives a positive value. And, in $9^3,$ base $\left(9\right)$ is positive. Therefore, $9^3$ has a positive value.

$\bullet$ $-6^8=-(6{)}^8.$ A positive base raised to any power gives always a positive value. Therefore, $6^8$ is a positive number. A positive number when multiplied by a negative number, it generates a negative value. Therefore, $-6^8$ is a negative number.

$\therefore$ $(-5{)}^2$ and $9^3$ have positive values, and $(-7{)}^3$ and $-6^8$ have negative values.