Questions · Page 2 of 2

1 Marks Question

Question 511 Mark
Find the value of $9^3$
Answer
In order to get the value of $9^3$, we should multiply $9$ three timesHence, $9^3=9 \times 9 \times 9=729$
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Question 521 Mark
Find the value of $2^6$
Answer
In order to get the value of $2^6$, we should multiply $2$ six timesHence $2^6=2 \times 2 \times 2 \times 2 \times 2 \times 2=64$
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Question 531 Mark
Expand: $\left(\frac{-4}{7}\right)^{5}$
Answer
Here, $\left(\frac{-4}{7}\right)^{5}=\frac{(-4)^{5}}{7^{5}}$ $=\frac{(-4) \times(-4) \times(-4) \times(-4) \times(-4)}{7 \times 7 \times 7 \times 7 \times 7}$
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Question 541 Mark
Expand: $\left(\frac{3}{5}\right)^{4}$
Answer
Here, $\left(\frac{3}{5}\right)^{4}=\frac{3^{4}}{5^{4}}=\frac{3 \times 3 \times 3 \times 3}{5 \times 5 \times 5 \times 5}$
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Question 551 Mark
Can you tell which one is greater $\left(5^2\right) \times 3$ or $\left(5^2\right)^3 $?
Answer
$\left(5^2\right) \times 3$ means $5^2$ is multiplied by $3$ i.e., $5 \times 5 \times 3=75$
but $\left(5^2\right)^3$ means $5^2$ is multiplied by itself three times i.e..
$5^2 \times 5^2 \times 5^2=5^6=15,625$
Therefore $\left(5^2\right)^3>\left(5^2\right) \times 3$
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Question 561 Mark
Which one is greater $2^3$ or $3^2$?
Answer
Here,
$2^3=2 \times 2 \times 2=8 \text { and }$
$3^2=3 \times 3=9$
Since $9>8$,
So, $3^2$ is greater than $2^3$
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Question 571 Mark
Express the number in the standard form: $70,040,000,000$
Answer
$70,040,000,000=7.004 \times 10,000,000,000=7.004 \times 10^{10}$
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Question 581 Mark
Express the number in the standard form: $3,430,000$
Answer
$3,430,000=3.43 \times 1,000,000=3.43 \times 10^6$
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Question 591 Mark
Express the number in the standard form: $65,950$
Answer
Here, $65,950=6.595 \times 10,000=6.595 \times 10^4$
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Question 601 Mark
Express the number in the standard form: $5985.3$
Answer
Here, $5985.3=5.9853 \times 1000=5.9853 \times 10^3$
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Question 611 Mark
Simplify: $2^3 \times a^3 \times 5 a^4$
Answer
Here,
$2^{3} \times a^{3} \times 5 a^{4}$
= $2^{3} \times a^{3} \times 5 \times a^{4}$
= $2^{3} \times 5 \times a^{3} \times a^{4}$
= $8 \times 5 \times a^{3+4}$
= $40a^7$
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Question 621 Mark
Simplify and write the answer in the exponential form: $8^2 \div 2^3$
Answer
Here, $8=2 \times 2 \times 2=2^3$
Thus, $8^2 \div 2^3=\left(2^3\right)^2 \div 2^3$
$=2^6 \div 2^3=2^{6-3}=2^3$
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Question 631 Mark
Simplify and write the answer in the exponential form: $\left[\left(2^2\right)^3 \times 3^6\right] \times 5^6$
Answer
Here,
${\left[\left(2^2\right)^3 \times 3^6\right] \times 5^6}$
$=\left[2^6 \times 3^6\right] \times 5^6$
$=(2 \times 3)^6 \times 5^6$
$=(2 \times 3 \times 5)^6=30^6$
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Question 641 Mark
Simplify and write the answer in the exponential form: $\left(6^2 \times 6^4\right) \div 6^3$
Answer
Here,
$\left(6^{2} \times 6^{4}\right) \div 6^{3}$
= $6^{2+4} \div 6^{3}$
$=\frac{6^{6}}{6^{3}}=6^{6-3}=6^{3}$
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Question 651 Mark
Simplify and write the answer in the exponential form: $2^3 \times 2^2 \times 5^5$
Answer
$\text { Here, } 2^3 \times 2^2 \times 5^5$
$=2^{3+2} \times 5^5$
$=2^5 \times 5^5$
$=(2 \times 5)^5$
$=10^5$
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Question 661 Mark
Simplify and write the answer in the exponential form: $\left(\frac{3^{7}}{3^{2}}\right) \times 3^{5}$
Answer
Here, $\left(\frac{3^{7}}{3^{2}}\right) \times 3^{5}=\left(3^{7-2}\right) \times 3^{5}$
$=3^5 \times 3^5$
$=3^{5+5}$
$=3^{10}$
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Question 671 Mark
Express $256$ as a power $2.$
Answer
Given number is, $256$
It can be expressed as,
$256=2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \text {. }$
So we can say that $256=2^8$
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1 Marks Question - Page 2 - Maths STD 7 Questions - Vidyadip