(a^m)^n=a^mn and a^0 = 1

Q.

Question 72

In the following question, state whether the given statements are true (T) or false (F).

$(-4{)}^{-4}\times (4{)}^{-1}=(4{)}^5$

Q. Simplify:

$\left(vi\right)$ $(125x^{-3}{)}^{\frac{1}{3}}$

Q.

Question 62

In the following question, fill in the blanks to make the statements true.

By solving $(6^0-7^0)\times (6^0+7^0)$, we get ___ .

Q.

Question 45

In the following question, fill in the blanks to make the statements true.

$[2^{-1}+3^{-1}+4^{-1}{]}^0=$ ___

Q.

Question 75

In the following question, state whether the given statements are true (T) or false (F).

$(-2{)}^0=2$

Q.

Question 78

In the following question, state whether the given statements are true (T) or false (F).

$(-7{)}^{-4}\times (-7{)}^2=(-7{)}^{-2}$

Q.

Question 20

In the following question, out of the four options, only one is correct. Write the correct answer:

$(-9{)}^3÷(-9{)}^8$ is equal to:
(a) $(9{)}^5$
(b) $(9{)}^{-5}$
(c) $(-9{)}^5$
(d) $(-9{)}^{-5}$

Q.

Question 64

In the following question, fill in the blanks to make the statements true.

The value of $(-7{)}^6÷7^6$ is ___ .

Q.

Question 42

In the following question, fill in the blanks to make the statements true.

$Bymultiplying\left(10{)}^{5}by\right(10{)}^{-10},weget$ ___

Q.

$(-1{)}^{-3}$ is:

___

Q.

$(-1{)}^{-3}$ is

__

Q.

Question 71

In the following question, state whether the given statements are true (T) or false (F).

$(-5{)}^{-2}\times (-5{)}^{-3}=(-5{)}^{-6}$

Q. Using the law of exponents, what is (a^-3 * b^-4)/(a^-2 * b^-3) in simplified terms?

1. a^5 b^7
2. ab^2
3. ab
4. 1/ab

Q. The multiplicative inverse of ${10}^{100}$ is

1. ${10}^{-100}$
2. $100$
3. ${10}^{100}$
4. $10$

Q. If $x={\left(\frac{-2}{5}\right)}^{30}÷{\left(\frac{-2}{5}\right)}^{28}$ and $y={\left(\frac{-2}{5}\right)}^2\times {\left(\frac{-2}{5}\right)}^3$, then find the value of $(x^3÷y{)}^2.$

1. $\frac{5}{40}$
2. $\frac{-2}{5}$
3. $\frac{4}{25}$
4. $\frac{25}{4}$

Q.

Simplify ${(2^5÷2^8)}^5$ × $2^{-5}.$

1. $\frac{1}{2^{10}}$

2. $\frac{1}{2^{(-15)}}$

3. $\frac{1}{2^{(-5)}}$

4. $\frac{1}{2^{20}}$

Q.

What is the value of ${\left(\right(2{)}^{-1})}^{-2}$ ?

__

Q. Solve for y if
$\frac{{\left(\frac{1}{9}\right)}^{2y-1}(.0081{)}^{\frac{1}{3}}}{\sqrt{243}}={\left(\frac{1}{3}\right)}^{2y-5}\sqrt[3]{3\frac{{27}^{y-1}}{10000}}$

1. $19\times 8$
2. $\frac{-19}{8}$
3. $\frac{18}{9}$
4. $\frac{-19}{18}$

Q.

Question 37

In the following question, fill in the blanks to make the statements true.

$5^5\times 5^{-5}$ =

Q.

Find the multiplicative inverse of ${10}^{-7}$.

1. ${10}^{-2}$

2. ${10}^2$

3. ${10}^7$

4. ${10}^6$

Q.

Simplify and write in exponential form: $4^3\times 4^{-2}\times {16}^2$

1. 4³

2. 4⁴

3. 4⁵

4. 4⁶

Q. Simplify $\frac{(-2{)}^3\times (-2{)}^7}{3\times 4^6}.$

1. 2
2. $\frac{1}{12}$
3. $\frac{2}{3}$
4. $\frac{1}{6}$

Q. Solve for $x$ in the equation $(-5{)}^{x+1}\times (-5{)}^5=(-5{)}^7$.

1. 2
2. 1
3. 7
4. 6

Q. What is $\frac{2^4}{2^1}$ equal to?

1. 2^3
2. 4^0
3. 2^4
4. 2^5

Q. Select the expression that is equivalent to ${10}^5\times {10}^7$.

1. ${10}^{-2}$
2. ${10}^2$
3. ${10}^{12}$
4. ${10}^{35}$