Power Law

Q.

If $3^{4x}=(81{)}^{-1}$ and $(10{)}^{\frac{1}{y}}=0.0001$, find the value of $2^{-x}\times {16}^y$

Q.

If $5^{x+1}={25}^{x-2}$; find the value of:

$3^{x-3}\times 2^{3-x}$

Q. If $(4^{\sqrt{x}}{)}^{\sqrt{x}}=256,$ then the value of $x$ is ___.

1. 16
2. 4
3. $\sqrt{2}$
4. 2

Q.

Find $x$ if $\sqrt{2^{x+3}}=16$.

1. 1

2. 0

3. 8

4. 5

Q.

Find the value of 'y' if $5^y=125$

1. 4

2. 3

3. 2

4. 5

Q.

Simplify and write in exponential form.
$(\frac{8^2}{8^5}{)}^4\times 8^{-3}$ [2 MARKS]

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.

Evaluate

$(\frac{a^m}{a^{-n}}{)}^{m-n}\times (\frac{a^n}{a^{-l}}{)}^{n-l}\times (\frac{a^l}{a^{-m}}{)}^{l-m}$

1. 0

2. a

3. 1

4. 2

Q.

Solve the equation:$3(2^x+1)-2^{x+2}+5=0$

Q.

Evaluate:

${(-17)}^3$.

Q.

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

1. True

2. False

Q.

Simplify and write the answer in the exponential form.

${\left(19\right)}^4\times {\left(19\right)}^2\times 19$

Q.

Solve:- $4^{x-2}-2^{x+1}=0$

1. 5

2. 6

3. -6

4. -5

Q.

Find the value of x if $2^x=32$.

1. 2

2. 4

3. 5

4. 6

Q.

The value of ${\frac{(-7)}{\left(7^6\right)}}^6$ is:

__

Q.

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

__

Q. Express each of the following in exponential notation $\left(\frac{-7}{13}\right)\times \left(\frac{-7}{13}\right)\times \left(\frac{-7}{13}\right)$.

Q.

By what number should we multiply $4^{-3}$ so that the product may be equal to 64?

1. $4^5$

2. $2^{12}$

3. $2^6$

4. $2^{1}0$

Q.

The value of ${\frac{(-7)}{\left(7^6\right)}}^6$ is: ___

Q.

Question 144

Fill in the blanks.

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. $x^4=16$, then $x=2$

1. True
2. False

Q. Express $\left[\right(2^3{)}^3{]}^2$ in exponential form.

Q. What is the value of $(5^2{)}^2+(2^2{)}^3$ ?

1. 689
2. 698
3. 589
4. 658

Q. Express in exponential form: ${\left(\frac{256}{84}\right)}^{\frac{5}{4}}$.

Q.

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

${(3\times 7)}^2$

Q.

Simplify $\frac{8}{x^2-4}-\frac{3}{x-2}$.

Q.

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

${(8\times 2)}^4$

Q. Find the value of: $\left[\right(-3{)}^{-4}÷(-3{)}^{-5}{]}^3$

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