a^m x b^m = (ab)^m

Q.

How do you simplify $8^{\frac{3}{4}}$ ?

Q.

If $m\ne n$ then $(m+n{)}^{-1}\times (m^{-1}+n^{-1})=$ ______

1. $mn$

2. 0

3. $m^{-1}{n}^{-1}$

4. $m^{-2}{n}^{-2}$

Q.

Find the value of 'a' satisfying the equation.
a) ${\left(4^2\right)}^a={\left(7^a\right)}^2$.
b) $(2^a{)}^5=2^4\times 4^3$
[4 MARKS]

Q.

$\frac{25}{16}$ in exponential form is _______.

1. 5³/4²

2. 5²/4³

3. 5³/4³

4. 5²/4²

Q.

Rina, being weak in Math asked for Tina’s help in preparing for exams.

Tina started by saying, $“3^2\times 3^2=3^4”$

Then she asked Rina to find the value of $“5^3\times 5^4”$ . Rina replied $5^{12}$ as the answer. Did she answer it correctly? (Yes/No)

1. Yes

2. No

Q. <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $x^a\times y^a=$ _____

1. $(xy{)}^{a+a}$
2. $(xy{)}^a$
3. $(x+y{)}^a$
4. $(x+y{)}^{a+a}$

Q. The value of ${(-2)}^4\times {\left(3\right)}^4$ is

1. $1296$
2. $1096$
3. -1296
4. -1096

Q.

Simplify and express in exponential form: $\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$ is :

1. $5^4$

2. $5^5$

3. $2^5$

4. $5^6$

Q.

The value of $(729{)}^{\frac{1}{3}}\times (64{)}^{\frac{1}{3}}$ is

1. 36

2. 18

3. 20

4. 30

Q. $2^5\times 4^5$ =

1. $8^5$
2. $8^{-5}$
3. ${24}^5$
4. -$8^5$

Q.

The value of $(343{)}^{\frac{1}{3}}\times (64{)}^{\frac{1}{3}}$ is

1. - 18

2. - 28

3. 18

4. 28

Q. ${(-2)}^4\times {\left(3\right)}^4$ = .

1. ${(-6)}^4$
2. $-{24}^4$
3. - ${12}^4$
4. - 1296

Q. Simplify ${12}^{-8}\times 5^{-8}$.

1. ${17}^{-8}$
2. ${60}^{-8}$
3. ${10}^{-8}$
4. ${60}^{-16}$

Q. The value of ${(-5)}^7\times {\left(2\right)}^7$ is

1. ${(-10)}^7$
2. ${\left(10\right)}^7$
3. ${\left(5\right)}^7$
4. ${(-2)}^7$

Q.

Find the value of $3^4\times 2^4$

1. 1200

2. 1296

3. 216

4. 1286

Q.

Evaluate $(3x^2{)}^{-3}\times (x^9{)}^{\frac{2}{3}}$

1. $\frac{-1}{9}$

2. $\frac{1}{9}$

3. $\frac{-1}{27}$

4. $\frac{1}{27}$

Q.

The value of $3\times (2{)}^{\frac{1}{3}}\times 7\times (6{)}^{\frac{1}{3}}\times 5\times (18{)}^{\frac{1}{3}}$ is

1. 545

2. 500

3. 630

4. 400

Q. $14x^3$ by $42x^2$

1. $\frac{x}{3}$
2. $\frac{x^2}{3}$
3. $\frac{x}{6}$
4. $None$

Q.

Using quotient law simplify $\frac{15a^2}{3a^5}$

1. 3a³

2. 5a⁵

3. 5/a³

4. 5/a⁵

Q. Match the values with the corresponding laws of exponents.

1. $2^4\times 3^4=6^4$
2. $\frac{4^7}{4^5}=4^2$
3. $3^7\times 3^2=3^9$
4. $(2^7{)}^4=2^{28}$

Q. Simplify $2^{-5}\times -5^{-5}$.

1. ${10}^{10}$
2. $-{10}^5$
3. $-2^7$
4. $-{10}^{-5}$

Q.

If $m\ne n$ then $(m+n{)}^{-1}\times (m^{-1}+n^{-1})=$ ______

1. 0

2. $mn$

3. $m^{-1}{n}^{-1}$

4. $m^{-2}{n}^{-2}$

Q. Find the value of ${(-2)}^4\times {\left(3\right)}^4$.

1. ${(-6)}^4$
2. $6^4$
3. - $6^4$
4. - 1296

Q.

Express the following in exponential form , using laws :

$\frac{{\left(x^{-2}\right)}^3\times {\left(y^2\right)}^3\times {\left(z^2\right)}^{-3}\times {\left(5^2\right)}^3}{{\left(2x^2\right)}^3\times {\left(y^{-3}\right)}^2\times {\left(-5\right)}^3}$

Q.

Find difference between :

$5^2$ and $2^5$.

Q. Simplify $2^{-5}\times -5^{-5}$.

1. $-{10}^5$
2. ${10}^{10}$
3. $-2^7$
4. $-{10}^{-5}$

Q.

$\frac{8}{27}={\left(\_\_\_\right)}^3$

Q. Find the value of the following:
${\left(\frac{-1}{2}\right)}^5$

Q. Verify the following:
(a) $18\times [7+(-3\left)\right]=[18\times 7]+[18\times (-3\left)\right]$
(b) $(-21)\times \left[\right(-4)+(-6\left)\right]=\left[\right(-21)\times (-4\left)\right]+\left[\right(-21)\times (-6\left)\right]$