Expanding a Rational Number Using Powers

Q. Express the value of 4 to the power 3.

1. 64
2. 16
3. 43
4. 12

Q. Number of prime factors in $(216{)}^{\frac{3}{5}}\times (2500{)}^{\frac{2}{5}}\times (300{)}^{\frac{1}{5}}$ is

1. 6
2. 7
3. 8
4. None of these

Q.

Question 172

Mass of Mars = $6.42\times {10}^{29}kg$ and Mass of the Sun = $1.99\times {10}^{30}kg$. What is the total mass ?

Q.

What is the value of -5 raised to the power of 2?

1. -25

2. 16

3. 5

4. 25

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. None of these

Q.

If( $-1$) is multiplied by itself ten times then we get $+1$

1. True
2. False

Q. 23.42 =
$2\times {10}^1+3\times {10}^0+4\times {10}^{-1}+2\times {10}^{-2}$

1. False
2. True

Q. 4009 written in the expanded form is

1. 4×103 + 9×101
2. 4×102 + 9×100
3. 4×103 + 9×100

Q.

If 3676.48 can be written in expanded form as:
$3\times {10}^a+b\times {10}^2+7\times {10}^c+6\times {10}^0+4\times {10}^d+e\times {10}^{-2}$ .
$\text{Find the value of}a+b-c-d-e.$

__

Q.

The product of $\frac{-2}{7}$and_____is $0$

Q.

What is the value of -5 raised to the power of 2?

1. -25

2. 16

3. 5

4. 25

Q. Question 2(a)
Find the number from each of the following expanded forms:
a) $8\times {10}^4+6\times {10}^3+0\times {10}^2+4\times {10}^1+5\times {10}^0$

Q. Express 16, 200 as a product of powers of prime numbers in the exponential form.

1. $2^3\times 3^3\times 5^4$
2. $2^3\times 3^3\times 5^3$
3. $2^4\times 3^3\times 5^3$
4. $2^3\times 3^4\times 5^2$

Q. What is the value of $\frac{\sqrt[3]{3125}+\sqrt[3]{3512}}{\sqrt[3]{3216}+\sqrt[2]{249}}$ ?

1. 0
2. 3
3. 1
4. 2

Q.

Simplify : $\left[\right\{(-5{)}^5\times (-5{)}^{-10}\}÷2^5]\times {10}^5$ [4 MARKS]

Q. Expanded form of $243.7=(2\times {10}^2)+(4\times {10}^1)+$ + $(7\times {10}^{-1}$)

1. $(4\times {10}^1)$
2. $(3\times {10}^1)$
3. $(3\times {10}^0)$
4. $(3\times {10}^2)$

Q.

Compare the following numbers :

$3.5\times {10}^2$ ; $2.76\times {10}^6$.

Q. Expanded form of $243.7=(2\times {10}^2)+(4\times {10}^1)+$ + $(7\times {10}^{-1}$)

1. $(4\times {10}^1)$
2. $(3\times {10}^1)$
3. $(3\times {10}^0)$
4. $(3\times {10}^2)$

Q. 32𝑚𝑛 divided by 8𝑛 gives

1. 4
2. 8𝑛
3. 8𝑚
4. 4𝑚

Q. $5\times {10}^2+6\times {10}^1+9\times {10}^0+2\times {10}^{-1}+2\times {10}^{-2}=$

1. $569.22$
2. 569.202
3. 569.022

Q.

If 3676.48 can be written in expanded form as:
$3\times {10}^a+b\times {10}^2+7\times {10}^c+6\times {10}^0+4\times {10}^d+e\times {10}^{-2}$ .
$\text{Find the value of}a+b-c-d-e.$

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Q. Write the following whole numbers in expanded form.

a) 18090

b) 3760

c) 94091

d) 90009 [4 MARKS]

Q. What is the value of $\frac{\sqrt[3]{3125}+\sqrt[3]{3512}}{\sqrt[3]{3216}+\sqrt[2]{249}}$ ?

1. 1
2. 2
3. 0
4. 3

Q. What is the value of $\frac{\sqrt[3]{3125}+\sqrt[3]{3512}}{\sqrt[3]{3216}+\sqrt[2]{249}}$ ?

1. 1
2. 2
3. 0
4. 3

Q. 23.42 =
$2\times {10}^1+3\times {10}^0+4\times {10}^{-1}+2\times {10}^{-2}$

1. False
2. True

Q.

Express $(3\times {10}^2)+(2\times {10}^1)+(9\times {10}^0)+(2\times {10}^{-1})+(5\times {10}^{-2})$ as a numeral.

1. 32.925

2. 3292.5

3. 329.25

4. 3.2925

Q. $\sqrt{49}$ = 7

1. False
2. True

Q.

Evaluate the expression ${(-4)}^2$.

Q.

What is the value of $\sqrt[3]{3\frac{0.027}{0.008}}+\sqrt[3]{3\frac{-0.027}{0.008}}+2?$

1. 2

2. 0

3. 1

4. -1

Q.

4329 = ___

1. $(9\times {10}^0)+(2\times {10}^1)+(3\times {10}^2)+(4\times {10}^3)$

2. $(4\times {10}^{-3})+(3\times {10}^1)+(2\times {10}^2)+(9\times {10}^3)$

3. $(4\times {10}^{-3})+(3\times {10}^{-2})+(2\times {10}^{-1})+(9\times {10}^0)$

4. $(9\times {10}^{-3})+(2\times {10}^{-2})+(3\times {10}^{-1})+(4\times {10}^3)$