Powers with Positive and Negative Exponents

Question 3 (i)
Simplify:

$2^{\frac{2}{3}}{.2}^{\frac{1}{5}}$

Express $8^{-2}$ as a exponent with base 2 :

1. $2^{-8}$

2. $8^{-4}$

3. $2^{-6}$

4. $2^{-4}$

1. $x^m$
   
   

2. $-x^m$
   

3. $\frac{1}{x^m}$
   

4. $\frac{-1}{x^m}$

$3^{-2}$ can be written as

1. $3{}^2$

2. $\frac{1}{3^2}$

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

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

If $x^a$ = $x^b$, then a = b. State whether true or false.

1. True

2. False

$\left(1^0+2^0+3^0\right)$ is equal to

1. $0$

2. $1$

3. $3$

4. $6$

Question 3 (iv)
Simplify:

$7^{\frac{1}{2}}{.8}^{\frac{1}{2}}$

The value of $3^5÷3^{-6}$ is

1. $3^5$

2. $3^{-6}$

3. $3^{11}$

4. $3^{-11}$

$5^5\times 5^{-5}=$ ______. Fill in the blank to make the statement true.

Solve $2^{2x+2}-6\times 2^x+2=0$

1. $x=-1orx=0$

2. $x=-1orx=1$

3. $x=-1orx=2$

4. $x=-2orx=0$

If ${\left(2^3\right)}^2$ is $2^x$, what is x?

1. 4

2. 5

3. 6

4. 7

Evaluate the expression.

$\frac{1}{7^9}·\frac{1}{7^6}$

If $3^x=\frac{1}{81}$, then the value of $x$ is

1. -4

2. -2

3. 4

4. 2

The value of $(\frac{5}{2}{)}^{-2}$ is $\frac{25}{4}$. State whether true or false.

1. True

2. False

Find the value of : $\frac{x^{a(b-c)}}{x^{b(a-c)}}÷(\frac{x^b}{x^a}{)}^c$

1. 0

2. b

3. a

4. 1

Fill in the blanks :

$2^4÷2^2\times 2^3=\_\_\_\_\_\_\_\_$

If $a^{n+2}$ = $a^{2n-1}$, the value of n is :

1. 1

2. 2

3. 3

4. 0

${(-\frac{5}{7})}^{-5}$ is equal to :

1. ${\left(\frac{5}{7}\right)}^{-5}$

2. ${\left(\frac{7}{5}\right)}^{-5}$

3. ${(-\frac{7}{5})}^{-5}$

4. ${(-\frac{7}{5})}^5$

1. $1$
2. $3$
3. $4$
4. $2$

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

1. 1

2. -1

3. 0

4. 2

Express $\frac{1}{81}$ in exponential form.

1. $3^{-4}$

2. $3^{-3}$

3. $3^4$

4. $3^3$

Evaluate ${\left(2^2\right)}^2$

Find the value of $3^2\times 3^{-5}$.

1. $3^{-3}$

2. $3^3$

3. $3^7$

4. $3^{-7}$

The value of $[4^{-1}+3^{-1}+6^{-2}{]}^{-1}$ is ___.

1. $\frac{36}{22}$

2. $\frac{38}{22}$

3. $\frac{36}{20}$

4. $\frac{36}{11}$

Find the value of $(\frac{1}{15}{)}^{-2}$ + $(\frac{1}{13}{)}^{-2}$ + $(\frac{1}{12}{)}^{-2}$.

1. 41

2. 538

3. 0.226

4. 269

Evaluate the value of the following:

$\frac{7^4\times 6^4}{{\left(42\right)}^2}$