Powers with Negative Bases

Q.

What is the highest power of $12$ that divides $54!$

1. $24$

2. $25$

3. $34$

4. $27$

Q. Match the expressions in the left column with their correct answers given in the right column.

1. $-729$
2. $216$
3. $-216$
4. $729$

Q. Match the following expressions with their correct values:

1. $-32$
2. $81$
3. $25$
4. $-64$

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

1. Negative
2. Positive
3. Cannot be determined

Q. Which of the following statement regarding the sign of $(-5{)}^{2021}$ is correct?

1. $(-5{)}^{2021}$ is a positive number.
2. $(-5{)}^{2021}$ is a negative number.

Q. For $a<0,$ select the correct statement(s).

1. $a^n=$ positive, if $n$ is even
2. $a^n=$ positive, if $n$ is odd
3. $a^n=$ negative, if $n$ is even
4. $a^n=$ negative, if $n$ is odd

Q. Check if the following relations are correct if $n$ represents an odd integer.

1. $-(-8{)}^n<0$
2. $-(-22{)}^{n-1}>0$
3. $(-5\times 3{)}^{n+1}<0$
4. $-(-4\times 5{)}^n>0$

Q. If $a$, $b$ are the integers other than zero, $m$ is an odd integer, the value of $(-a\times b{)}^m$ for $a=1$, $b=2$ and $m=3$ is

1. $-8$
2. $8$
3. $16$
4. $-16$