Power Rule of Exponents

Q.

Simplify: $\frac{{11}^{{\displaystyle \frac{1}{2}}}}{{11}^{{\displaystyle \frac{1}{4}}}}$

Q. Find the value of $({36}^3{)}^{-3}$.

1. $\left({36}^{-9}\right)$
2. $\left({36}^9\right)$
3. $\left(6^{18}\right)$
4. $\left(6^{-18}\right)$

Q. $(-6{)}^{-82}\times (81{)}^{-41}$ =

1. $(-36{)}^{-41}$
2. $(-486{)}^{-82}$
3. $(-87{)}^{-82}$
4. $(-54{)}^{-82}$

Q. $(a^m{)}^n=$ _____

1. $a^{m+n}$
2. $a^{mn}$
3. $a^{m-n}$
4. $mn\times a$

Q. Solve:
$\frac{5^{\frac{1}{3}}\times 5^2\times 5^{\frac{-1}{2}}}{5^{\frac{4}{5}}÷\sqrt{5}÷5^{\frac{2}{5}}}\times \frac{5^{\frac{4}{3}}}{5^{\frac{1}{10}}}$

1. $5^{\frac{11}{3}}$
2. $5^{\frac{10}{3}}$
3. $5^{-\frac{10}{3}}$
4. $5^{\frac{12}{3}}$

Q.

Complete the table by finding the sum and the difference of Expression 1 and Expression 2.

Write your answers in scientific notation. Explain your method.

Q.

The value of ${\left({\left(2^2\right)}^2\right)}^2$ is:

1. $2^6$

2. $2^{16}$

3. $2^8$

4. $2^4$

Q.

Simplify the following and write the answer in the exponential notation.

${(3\times 9)}^3$

Q. Simplify $6^{24}÷6^9$ and write the answer in exponential form.
[1 mark]

Q. Find the value(s) of $(5^{-3}{)}^2$.

1. -$\frac{1}{5^6}$
2. $\frac{1}{5^6}$
3. $(-5{)}^{-6}$
4. $\left(5^{-6}\right)$

Q. The value of ${\left(\right(2{)}^{-1})}^{-2}$ is .

1. $\frac{1}{4}$
2. 4
3. 16
4. $4^{-2}$

Q. The value of $({\left(\frac{3}{2}{)}^{-1}\right)}^{-2}$ is .

1. $\frac{4}{9}$
2. $\frac{-4}{9}$
3. $\frac{-9}{4}$
4. $\frac{9}{4}$

Q.

${\left({12}^5\right)}^6$ = ${12}^{56}$

1. True

2. False

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. Find the value(s) of $(5^{-3}{)}^2$.

1. -$\frac{1}{5^6}$
2. $\frac{1}{5^6}$
3. $(-5{)}^{-6}$
4. $\left(5^{-6}\right)$

Q.

Evaluate $(1^3+2^3+3^3+4^3{)}^{\frac{-3}{2}}.$

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

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

3. ${10}^{-3}$

4. ${10}^{-4}$

Q.

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

1. 28

2. - 28

3. 18

4. - 18

Q.

Find the value of x if $\frac{8^2}{5^6}={\left(\frac{x}{5}\right)}^6$

1. 4

2. 8

3. 2

4. 16

Q.

Evaluate $(3x^4{)}^{-2}\times (x^{12}{)}^{\frac{2}{3}}$

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

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

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

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