2 Marks Questions

Question 12 Marks

Write the following numbers in the expanded forms.
20072

Answer

Expanded form of 20068
$=2 \times 10000+0 \times 1000+0 \times 100+6 \times 10+8 \times 1$
$=2 \times 10^4+0 \times 10^3+0 \times 10^2+6 \times 10^1+8 \times 10^0$ $\left[\because 10^{\circ}=1\right]$

View full question & answer→

Question 22 Marks

Write the following numbers in the expanded forms.
120719

Answer

Expanded form of 120719
$=1 \times 100000+2 \times 10000+0 \times 1000+7$ $\times 100+1 \times 10+9 \times 1$
$=1 \times 10^5+2 \times 10^4+0 \times 10^3+7 \times 10^2+1 \times 10^1$ $+9 \times 10^0 \quad\left[\because 10^0=1\right]$

View full question & answer→

Question 32 Marks

Write the following numbers in the expanded forms.
2806196

Answer

Expanded form of 2806196
$=2 \times 1000000+8 \times 100000+0 \times 10000+6 \times 1000$ $+1 \times 100+9 \times 10+6 \times 1$
$=2 \times 10^6+8 \times 10^5+0 \times 10^4+6 \times 10^3$ $+1 \times 10^2+9 \times 10^1+6 \times 10^0$ $\left[\because 10^0=1\right]$

View full question & answer→

Question 42 Marks

Write the following numbers in the expanded forms.
3006194

Answer

Expanded form of 3006194
$=3 \times 1000000+0 \times 100000+0 \times 10000$ $+6 \times 1000+1 \times 100+9 \times 10+4 \times 1$
$=3 \times 10^6+0 \times 10^5+0 \times 10^4+6 \times 10^3$ $+1 \times 10^2+9 \times 10^1+4 \times 10^0 \quad\left[\because 10^0=1\right]$

View full question & answer→

Question 52 Marks

Write the following numbers in the expanded forms.
279404

Answer

Expanded form of 279404
$=2 \times 100000+7 \times 10000+9 \times 1000+4 \times 100$ $+0 \times 10+4 \times 1$
$=2 \times 10^5+7 \times 10^4+9 \times 10^3+4 \times 10^2+0 \times 10^1$ $+4 \times 10^0 \quad\left[\because 10^0=1\right]$

View full question & answer→

Question 62 Marks

Expand by expressing powers of 10 in the exponential form :
$1,76,428$

Answer

Expanded form of $1,76,428$
$=1 \times 100000+7 \times 10000+6 \times 1000+4 \times 100$$+2 \times 10+8 \times 1$
$=1 \times 10^5+7 \times 10^4+6 \times 10^3+4 \times 10^2$$+2 \times 10^1+8 \times 10^0$
which is the required exponential form in powers of 10.

View full question & answer→

Question 72 Marks

Expand by expressing powers of 10 in the exponential form :
56,439

Answer

Expanded form of 56,439
$\begin{array}{l}=5 \times 10000+6 \times 1000+4 \times 100+3 \times 10+9 \times 1 \\ =5 \times 10^4+6 \times 10^3+4 \times 10^2+3 \times 10^1+9 \times 10^0\end{array}$
which is the required exponential form in powers of 10.

View full question & answer→

Question 82 Marks

Expand by expressing powers of 10 in the exponential form :
5,643

Answer

Expanded form of 5,643
$\begin{array}{l}=5 \times 1000+6 \times 100+4 \times 10+3 \times 1 \\ =5 \times 10^3+6 \times 10^2+4 \times 10^1+3 \times 10^0\end{array}$
which is the required exponential form in powers of 10.

View full question & answer→

Question 92 Marks

Expand by expressing powers of 10 in the exponential form :
172

Answer

Expanded form of
$172=1 \times 100+7 \times 10+2 \times 1$
$=1 \times 10^2+7 \times 10^1+2 \times 10^0$ $\left[\because 10^{\circ}=1\right]$
which is the required exponential form in powers of 10.

View full question & answer→

Question 102 Marks

Using laws of exponents, simplify and write the answer in exponential form.
$\left(3^4\right)^3$

Answer

$\left(3^4\right)^3=3^{4 \times 3}=3^{12}$ $\left[\because\left(a^m\right)^n=a^{m n}\right]$

View full question & answer→

Question 112 Marks

Using laws of exponents, simplify and write the answer in exponential form.
$\left(5^2\right)^3+5^3$

Answer

$\left(5^2\right)^3+5^3=5^{2 \times 3}+5^3$ $\left[\because\left(a^m\right)^n=a^{m n}\right]$
$=5^6+5^3=5^{6-3}=5^3$ $\left[\because a^m+a^n=a^{m-n}\right]$

View full question & answer→

Question 122 Marks

Using laws of exponents, simplify and write the answer in exponential form.
$6^{15}+6^{10}$

Answer

$6^{15}+6^{10}=6^{15-10}=6^5$ $\left[\because a^m+a^n=\frac{a^m}{a^n}=a^{m-n}\right]$

View full question & answer→

Question 132 Marks

Using laws of exponents, simplify and write the answer in exponential form.
$3^2 \times 3^4 \times 3^8$

Answer

$3^2 \times 3^4 \times 3^8=\left(3^{2+4}\right) \times 3^8$ $\left[\because a^m \times a^n=a^{m * n}\right]$
$=3^6 \times 3^8=3^{6+8}=3^{14}$

View full question & answer→

Question 142 Marks

Simplify:
$(-2)^3 \times(-10)^3$

Answer

We have,
$(-2)^3 \times(-10)^3$
= (-2) × (-2) × (-2) × (-10) × (-10) × (-10)
= (-8) × (-1000) = 8000
Hence, the value of $(-2)^3 \times(-10)^3$ is 8000.

View full question & answer→

Question 152 Marks

Simplify:
$(-3)^2 \times(-5)^2$

Answer

We have,
$(-3)^2 \times(-5)^2$
= (-3) × (-3) × (-5) × (-5)
= 9 × 25 = 225
Hence, the value of $(-3)^2 \times(-5)^2$ is 225.

View full question & answer→

Question 162 Marks

Simplify:
$(-3) \times(-2)^3$

Answer

We have,
$(-3) \times(-2)^3$
= (-3) × (-2) × (-2) × (-2) = (-3) × (-8) = 24
Hence, the value of $(-3) \times(-2)^3$ is 24.

View full question & answer→

Question 172 Marks

Simplify:
$(-4)^3$

Answer

We have,
$(-4)^3=(-4) \times(-4) \times(-4)$
= 16 × (-4) = -64
Hence, the value of $(-4)^3$ is -64.

View full question & answer→

Question 182 Marks

Simplify:
$3^2 \times 10^4$

Answer

We have,
$3^2 \times 10^4=3 \times 3 \times 10 \times 10 \times 10 \times 10$
= 9 × 10000 = 90000
Hence, the value of $3^2 \times 10^4$ is 90000.

View full question & answer→

Question 192 Marks

Simplify:
$2^4 \times 3^2$

Answer

We have,
$2^4 \times 3^2=2 \times 2 \times 2 \times 2 \times 3 \times 3=16 \times 9=144$
Hence, the value of $2^4 \times 3^2$ is 144.

View full question & answer→

Question 202 Marks

Simplify:
$5^2 \times 3^3$

Answer

We have,
$5^2 \times 3^3=5 \times 5 \times 3 \times 3 \times 3=25 \times 27=675$
Hence, the value of $5^2 \times 3^3$ is 675.

View full question & answer→

Question 212 Marks

Simplify:
$0 \times 10^2$

Answer

We have,
$0 \times 10^2=0 \times(10 \times 10)=0 \times 100=0$
Hence, the value of $0 \times 10^2$ is 0.

View full question & answer→

Question 222 Marks

Simplify:
$3 \times 4^4$

Answer

We have,
$3 \times 4^4=3 \times 4 \times 4 \times 4 \times 4=3 \times 256=768$
Hence, the value of $3 \times 4^4$ is 768.

View full question & answer→

Question 232 Marks

Simplify:
$2^3 \times 5$

Answer

We have,
$2^3 \times 5=2 \times 2 \times 2 \times 5=8 \times 5=40$
Hence, the value of $2^3 \times 5$ is 40.

View full question & answer→

Question 242 Marks

Simplify:
$7^2 \times 2^2$

Answer

We have,
$7^2 \times 2^2=7 \times 7 \times 2 \times 2=49 \times 4=196$
Hence, the value of $7^2 \times 2^2$ is 196.

View full question & answer→

Question 252 Marks

Simplify:
$2 \times 10^3$

Answer

We have,
$2 \times 10^3=2 \times(10 \times 10 \times 10)=2 \times 1000=2000$
Hence, the value of $2 \times 10^3$ is 2000.

View full question & answer→

Question 262 Marks

Identify the greater number, wherever possible, in each of the following?
$4^3$ or $3^4$

Answer

We have, $4^3$ or $3^4 \Rightarrow 4^3=4 \times 4 \times 4=64$
[here, multiply base = 4 three times, since exponent = 3]
and $3^4=3 \times 3 \times 3 \times 3=81$
(here, multiply base = 3 four times, since exponent = 4 ]
$\because \quad 81>64$
$\Rightarrow$ $3^4>4^3$
Hence, $3^4$ is greater than $4^3$.

View full question & answer→

Question 272 Marks

Express each of the following numbers using exponential notation.
3125

Answer

We have, $3125=5 \times 5 \times 5 \times 5 \times 5=5^5$
Hence, the exponential form of 3125 is $5^5$.

View full question & answer→

Question 282 Marks

Express each of the following numbers using exponential notation.
729

Answer

We have, $729=3 \times 3 \times 3 \times 3 \times 3 \times 3=3^6$
Hence, the exponential form of 729 is $3^6$.

View full question & answer→

Question 292 Marks

Express each of the following numbers using exponential notation.
343

Answer

We have, $343=7 \times 7 \times 7=7^3$
Hence, the exponential form of 343 is $7^3$.

View full question & answer→

Question 302 Marks

Express each of the following numbers using exponential notation.
512

Answer

We have,
$512=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2=2^9$
Hence, the exponential form of 512 is $2^9$.

View full question & answer→

Question 312 Marks

Find the value of:
$2^6$

Answer

$2^6=2 \times 2 \times 2 \times 2 \times 2 \times 2=64$
Hence, the value of $2^6$ is 64.

View full question & answer→

Question 322 Marks

Find the difference between $5^3$ and $2^4$.

Answer

Given, $5^3$ and $2^4$
$\because \quad 5^3=5 \times 5 \times 5=125$
and $2^4=2 \times 2 \times 2 \times 2=16$
$\therefore \quad 5^3-2^4=125-16=109$

View full question & answer→

Question 332 Marks

Write $m \times m \times m \times m \times m \times m \times n \times n$ in exponential form.

Answer

Given, $m \times m \times m \times m \times m \times m \times n \times n$
$\because m \times m \times m \times m \times m \times m=m^6$ and $n \times n=n^2$
So, $m \times m \times m \times m \times m \times m \times n \times n=m^6 \times n^2=m^6 n^2$

View full question & answer→

Question 342 Marks

Express $(-128)$ as powers of $(-2)$.

Answer

We have,-128
$\begin{array}{l}=(-2) \times(-2) \times(-2) \times(-2) \times(-2) \times(-2) \times(-2) \\ =(-2)^7\end{array}$

View full question & answer→

Question 352 Marks

Express the following numbers in standard form.
3908.78

Answer

We know that in standard form; any number is expressed as decimal number between 1.0 and 10.0 multiplied by a power of 10 . Then, the standard form of given numbers are given below.
We have, 3908.78
$3908.78=3.90878 \times 1000=3.90878 \times 10^3$

View full question & answer→

Question 362 Marks

Express the following numbers in standard form.
39087.8

Answer

We know that in standard form; any number is expressed as decimal number between 1.0 and 10.0 multiplied by a power of 10 . Then, the standard form of given numbers are given below.
We have, 39087.8
$39087.8=3.90878 \times 10000=3.90878 \times 10^4$

View full question & answer→

Question 372 Marks

Express the following numbers in standard form.
390878

Answer

We know that in standard form; any number is expressed as decimal number between 1.0 and 10.0 multiplied by a power of 10 . Then, the standard form of given numbers are given below.
We have, 390878
$390878=3.90878 \times 100000=3.90878 \times 10^5$

View full question & answer→

Question 382 Marks

Express the following numbers in standard form.
3186500000

Answer

We know that in standard form; any number is expressed as decimal number between 1.0 and 10.0 multiplied by a power of 10 . Then, the standard form of given numbers are given below.
We have, 3186500000
$3186500000=3.1865 \times 1000000000=3.1865 \times 10^9$

View full question & answer→

Question 392 Marks

Express the following numbers in standard form.
7000000

Answer

View full question & answer→

Question 402 Marks

Express the following numbers in standard form.
50000000

Answer

We know that in standard form; any number is expressed as decimal number between 1.0 and 10.0 multiplied by a power of 10 . Then, the standard form of given numbers are given below.
We have, 50000000
$50000000=5.0 \times 10000000=5 \times 10^7$

View full question & answer→

Question 412 Marks

Find the number from each of the following expanded forms.
$4 \times 10^5+5 \times 10^3+3 \times 10^2+2 \times 10^0$

Answer

$4 \times 10^5+5 \times 10^3+3 \times 10^2+2 \times 10^0$
$=4 \times 100000+5 \times 1000+3 \times 100+2 \times 1\left[\because 10^0=1\right]$
$=4 \times 100000+0 \times 10000+5 \times 1000+3 \times 100$ $+0 \times 10+2 \times 1$
$=405302$ [here, $10^4$ and $10^1$ are missing, so take these terms with multiply zero]

View full question & answer→

Question 422 Marks

Find the number from each of the following expanded forms.
$8 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0$

Answer

$8 \times 10^4+6 \times 10^3+0 \times 10^2+4 \times 10^1+5 \times 10^0$
$=8 \times 10000+6 \times 1000+0 \times 100+4 \times 10+5 \times 1$
= 86045 $\left[\because 10^0=1\right]$

View full question & answer→

Question 432 Marks

Simplify :
$\frac{\left(2^5\right)^2 \times 7^3}{8^3 \times 7}$

Answer

We have,
$\frac{\left(2^5\right)^2 \times 7^3}{8^3 \times 7}=\frac{2^{5 \times 2} \times 7^3}{\left(2^3\right)^3 \times 7}$ $\left[\because 8=2 \times 2 \times 2=2^3\right.$ and $\left.\left(a^m\right)^n=a^{m n}\right]$
$=\frac{2^{10} \times 7^3}{2^9 \times 7^1}=2^{10-9} \times 7^{3-1}$ $\left[\because a^m \div a^n=a^{m-n}\right]$
$=2^1 \times 7^2=2 \times 7^2=2 \times 7 \times 7=98$

View full question & answer→

MATHS 2 Marks Questions

Test yourself on this topic