Question

What is the sign of $(-5{)}^9\times {27}^3?$

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

Answer 1

The correct option is A Negative

$\underset{–}{\text{Need to find:}}$ Sign of $(-5{)}^9\times {27}^3$

$\underset{–}{\text{Method-1}:}$
In $(-5{)}^9\times {27}^3,$ $(-5{)}^9$ is negative and ${27}^3$ is positive. Because as we know,

• A negative base raised to an odd power is negative.
• A positive base raised to any power is positive.

And, a positive number when multiplied by a negative number always gives a negative value. Therefore, $(-5{)}^9\times {27}^3$ is negative.

$\underset{–}{\text{Method-2}:}$
$(-5{)}^9\times {27}^3$
$=(-5{)}^9\times (3^3{)}^3$
[As $27=3\times 3\times 3=3^3$]

$=(-5{)}^9\times 3^{3\times 3}$
$[\because (a^m{)}^n=a^{m\times n}]$

$=(-5{)}^9\times 3^9$
[ Multiplying exponents with different bases but same exponent: $a^n\times b^n=(a\times b{)}^n$ ]

$=(-5\times 3{)}^9$
$=(-15{)}^9$

A negative base raised to an odd power always gives a negative value.

Therefore, $(-15{)}^9$ is a negative number, i.e., the sign of $(-5{)}^9\times {27}^3$ is also negative.

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