Question

What is the sign of the exponent $(-7{)}^3\times (-7{)}^5?$

• A. Negative
• B. Positive
• C. Cannot be determined

Answer 1

The correct option is B Positive

$\underset{–}{\text{Need to find:}}$ Sign of $(-7{)}^3\times (-7{)}^5$

$(-7{)}^3\times (-7{)}^5$
[ <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Multiplying exponents with same base: $a^m\times a^n=a^{m+n}$ ]

$=(-7{)}^{3+5}$
$=(-7{)}^8$

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, in $(-7{)}^8,$ base $(-7)$ is negative and exponent $\left(8\right)$ is even. Therefore, $(-7{)}^8$ has a positive value.

$\therefore$ Option (b.) is the correct one.