Powers and Exponents

Q.

Name the property under multiplication used in each of the following:

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

(ii) $\frac{-13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{7}$

(iii) $\frac{-19}{29}\times \frac{29}{-19}=1$

Q.

Question 177(iii)

Find x.
$2^x+2^x+2^x=192$

Q.

If $(2^{3x-1}+10)÷7=6$, then $x$ is equal to

(a) $-2$

(b) $0$

(c) $1$

(d) $2$

Q.

$256$ expressed as a power of $2.$

Q.

$128$ expressed as a power of $2.$

Q. Find the square root of: 4.84

1. 2.2
2. 3.2
3. 2.1
4. 2.4

Q.

Express $2$ x $2$ x$2$ x$2$ x$2$ x$2$ in exponential form

1. 4³

2. 4⁴

3. 4⁵

4. 4⁶

Q. If $a\ne 0,$ then the value of $a^0$ is .

1. \N
2. 1
3. 2
4. -1

Q. Find the product of $\frac{6}{13}$ and multiplicative inverse of $\frac{-1}{4}$.

1. $\frac{-3}{26}$
2. $\frac{3}{26}$
3. $\frac{-24}{13}$
4. $\frac{24}{13}$

Q. The multiplicative inverse of a number $-n$ is .

Q.

The number of ways of dividing $15$ men and $15$ women into $15$ couples each consisting of a man and a woman is?

1. $1240$

2. $1840$

3. $1820$

4. $2005$

Q.

Question 179(i)

Express each of the following in exponential form.
$\frac{-1296}{14641}$

Q.

${[2^{-1}+3^{-1}+4^{-1}]}^0=\_\_\_\_\_\_$. Fill in the blank to make the statement true.

Q.

Write $2187$ in exponential form & identify the base & exponent.

Q. For a fixed base, if the exponent decreases by 1, the number becomes

1. One-tenth of the previous number
2. Ten times of the previous number
3. Hundred times of the previous number
4. Hundredth of the previous number

Q.

The value of ${1000}^{\circ }$ is 1000.

1. True

2. False

Q.

For a fixed base $10$, if the exponent decreases by $1$, the number becomes:

1. One-tenth of the previous number

2. Ten times of the previous number

3. Hundredth of the previous number

4. Hundred times of the previous number

Q. Find the cube of 0.3

1. 0.27
2. 0.027
3. 0.0027
4. 0.00027

Q.

Question 128(iii)

Predicting the ones digit, copy and complete this table and answer the questions that follow.

Powers Table
$\begin{array}{ccccccccccc}X& 1^x& 2^x& 3^x& 4^x& 5^x& 6^x& 7^x& 8^x& 9^x& {10}^x\\ 1& 1& 2& & & & & & & & \\ 2& 1& 4& & & & & & & & \\ 3& 1& 8& & & & & & & & \\ 4& 1& 16& & & & & & & & \\ 5& 1& 32& & & & & & & & \\ 6& 1& 64& & & & & & & & \\ 7& 1& 128& & & & & & & & \\ 8& 1& 256& & & & & & & & \\ Onesdigitsofthepowers& 1& 2,4,6,8& & & & & & & & \end{array}$

Predict the ones digit in the following.
$\left(i\right){31}^{10}$
$\left(ii\right){12}^{10}$
$\left(iii\right){17}^{21}$
$\left(iv\right){29}^{10}$

Q.

The value of $4^0$ is _________

1. 1

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

Q.

Find the cube root $\sqrt[3]{-\frac{343}{1000}}$.

Q. The multiplicative inverse of 15/2 is ____.

1. -1
2. 0
3. 1
4. 2/15

Q.

Question 140(ii)

Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression $3^{-t}$.
After how many half-lives will the fraction be $\frac{1}{243}$ of the original?

Q.

Express the number $343$ using exponential notation

Q.

Question 124(ii)

The cell of a bacteria doubles in every 30 min. A scientist begins with a single cell. How many cells will be thereafter 24h?

Q. Why should the power of an exponent in a variable always be a whole number?

Q. What value of x makes "3 to the x power = 81" a true statement?

1. 3
2. 27
3. 9
4. 4

Q.

For representing the multiplicative inverse of 5/7 on the number line, one unit should be divided in how many parts?

1. 5

2. 8

3. 7

4. 6

Q.

State whether the given statement is True or False: ${(10+10)}^{10}={10}^{10}+{10}^{10}$.

1. True
2. False

Q.

If $4^x$ = 64, then which of the following is/are true?

1. $2^x=8$

2. $3^x=27$

3. $x^3=9$

4. ${10}^x$=10000