Exponents - ICSE STD 7 MATHS Questions

Q 1[2 Mark Question Answer]2 Marks

Express in exponential notation : $\left(\frac{1}{24}\right)^{13} \div\left(\frac{1}{24}\right)^{16}$

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Q 2[2 Mark Question Answer]2 Marks

Express in exponential notation : $\left(\frac{-7}{15}\right)^{12}+\left(\frac{-7}{15}\right)^{15}$

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Q 3[2 Mark Question Answer]2 Marks

Express in exponential notation : $\left(\frac{-16}{35}\right)^{16} \div\left(\frac{-16}{35}\right)^3$

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Q 4[2 Mark Question Answer]2 Marks

Express in exponential notation : $\left(\frac{13}{43}\right)^7 \div\left(\frac{13}{43}\right)^2$

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Q 5[2 Mark Question Answer]2 Marks

Express in exponential notation : $\left(\frac{-7}{3}\right)^{11} \times\left(\frac{-7}{3}\right)^{13}$

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Q 6[3 marks sum]3 Marks

In a tennis competition, 128 players were selected for a series of knockout rounds. In each round the losers were eliminated and the winners reached the next round. How many players moved to the next round after 4th round? Express this number in the exponential notation in terms of the initial number of players.

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Q 7[4 marks sum]4 Marks

In a bacteria culture under observation in a laboratory, the population of 50 bacteria doubles itself every hour.
Q.1. Which of the following expressions gives the bacterial population after n hours?
(a) $\frac{50}{2^n}$$\quad$$\quad$ (b) $25^n$ $\quad$$\quad$(c) $50 \times 2^n$$\quad$$\quad$ (d) $\frac{50^n}{2}$
Q.2. The population size of the bacteria after 3 hours will be
(a) 200 $\quad$$\quad$(b) 300 $\quad$$\quad$(c) 400 $\quad$$\quad$(d) 500
Q.3. How many bacteria will be there in the culture after 1 day?
(a) $\frac{50}{2^{12}}$ $\quad$$\quad$(b) $50 \times 2^{24}$$\quad$$\quad$ (c) $50 \times \times 2^{12}$ $\quad$$\quad$(d) $\frac{50}{2^{24}}$
Q.4. If the culture is observed after every one hour, find the number of hours after which the population size of the bacteria will be larger than 1000.
(a) 5 $\quad$$\quad$(b) 6 $\quad$$\quad$(c) 8 $\quad$$\quad$(d) 10

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Q 8[4 marks sum]4 Marks

A computer purchased for ₹ 72900 loses two-third of its value every year. Its value is evaluated at the end of every year.
Q.1. Which of the following expressions gives the value of the computer (in ₹) after n years?
(a) $\frac{72900}{\left(\frac{2}{3}\right)^n}$ $\quad$$\quad$(b) $\frac{2^n \times 27900}{3^n}$ $\quad$$\quad$(c) $\frac{72900}{3^n}$ $\quad$$\quad$ (d) $\frac{72900}{2^n \times 3^n}$
Q.2. Find the value of the computer after 3 years.
(a) ₹ 8100 $\quad$$\quad$(b) ₹ 2430 $\quad$$\quad$(c) ₹ 5600$\quad$$\quad$ (d) ₹ 2700
Q.3. In how many years will the value of the computer be less than ₹ 200?
(a) 6 years $\quad$$\quad$(b) 7 years $\quad$$\quad$(c) 8 years $\quad$$\quad$(d) 10 years
Q.4. By how much will the value of the computer reduce in 4 years?
(a) ₹ 24300 $\quad$$\quad$(b) ₹ 1800 $\quad$$\quad$(c) ₹ 8100 $\quad$$\quad$(d) ₹ 72000

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Q 9TRUE / FALSE1 Mark

In an exponential notation $x^n ; n$ is called the index.

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Q 10TRUE / FALSE1 Mark

If a number p is multiplied n times, then the resulting number is $p^n.$

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Q 11TRUE / FALSE1 Mark

For a non-zero number $x ;\left(x^m \times x^n\right)$ is equal to x to the power (m + n).

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Q 12TRUE / FALSE1 Mark

If a and b are non-zero numbers, then $\{$${(\frac{a}{b})^{m}}$$\}^{n}=(\frac{b}{a})^{-mn}$