Exercise 5A
Q1 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 1
Fill in the blanks :
| Expression | Meaning | Exponent | Base | Value |
|---|---|---|---|---|
| (i) $5^3$ | 5×5×5 | |||
| (ii) $(-9)^2$ | ||||
| (iii) $\left(\frac{3}{5}\right)^3$ | 3 | |||
| (iv) $\left(\frac{-2}{3}\right)^5$ | 5 | $\frac{-2}{3}$ |
Sol :
| Expression | Meaning | Exponent | Base | Value |
|---|---|---|---|---|
| (i) $5^3$ | 5×5×5 | 3 | 5 | 125 |
| (ii) $(-9)^2$ | -9×9 | 2 | -9 | 81 |
| (iii) $\left(\frac{3}{5}\right)^3$ | $\frac{3}{5}\times \frac{3}{5}\times \frac{3}{5}$ | 3 | $\frac{3}{5}$ | $\frac{27}{125}$ |
| (iv) $\left(\frac{-2}{3}\right)^5$ | $\frac{-2}{5} \times\frac{-2}{5} \times \frac{-2}{5} \times \frac{-2}{5} \times \frac{-2}{5} \times $ | 5 | $\frac{-2}{3}$ | $\frac{-32}{243}$ |
Q2 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 2
State the exponential form of each expression :
(i) $8 \times 8 \times 8 \times 8 \times 8 \times 8$
Sol: $=8^{6}$
(ii) $-6 \times -6 \times -6 \times -6$
Sol: $-6^{4}$
(iii) $x \times x \times x \times x \times x \times x \times x$
Sol: $x^{7}$
(iv) $\frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3}=$
Sol: $\left(\frac{2}{3}\right)^{5}$
(v) $-2 \times-2 \times-2 \times 3 \times 3$
Sol: $(-2)^{3} \times 3^{2}$
(vi) $3 \times 3 \times 11 \times 11 \times 11$
Sol: $3^{2} \times 11^{3}$
Q3 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 3
Write the expended form of :
(i) $4^{6}$
Sol: $4 \times 4 \times 4 \times 4 \times 4 \times 4$
(ii) $(-7)^{3}$
Sol: $-7 \times -7 \times -7$
(iii) $\left(\frac{1}{3}\right)^{5}$
Sol: $=\frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}$
(iv) $\left(\frac{-3}{4}\right)^{4}$
Sol: $\frac{-3}{4} \times \frac{-3}{4} \times \frac{-3}{4} \times \frac{-3}{4}$
(v) $(-37)^{2} \times 4^{4}$
Sol: $-37 \times -37 \times 4 \times 4 \times 4 \times 4$
Q4 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 4
Express in power notation :
prime factorization
(i) 125
Sol: $\begin{array}{l|l}5 & 125 \\\hline 5 & 25 \\\hline 5 & 5 \\\hline &1\end{array}$
$5 \times 5 \times 5$
$5^{3}$
(ii) 256
Sol: $\begin{array}{c|c}2 & 256 \\\hline2 & 128 \\\hline 2 & 64 \\\hline 2 & 32 \\\hline 2 & 16 \\\hline 2 & 8 \\\hline 2 & 4 \\\hline 2 & 2\end{array}$
=$2^{8}$
(iii) -343
Sol: $\begin{array}{c|c}7 & 343 \\\hline 7 & 49 \\\hline 7 & 7 \\\hline & 1\end{array}$
$-7^{3}$
(iv) $\frac{49}{25}$
Sol: $\frac{7^{2}}{5^{2}}=\left(\frac{7}{5}\right)^{2}$
(v) $\frac{-8}{27}=\frac{-2^{3}}{3^{3}}=-\left(\frac{2}{3}\right)^{3}$
Q5 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 5
Find the value of :
(i) $(-5)^{3} \times(-1)^{7} \times 2^{2}$
= $-5 \times -5 \times -5 \times-1 \times 2 \times 2$
=$125 \times 4$
=500
(ii) $\left(\frac{1}{3}\right)^{3} \times\left(\frac{3}{5}\right)^{2}$
Sol: $\frac{1}{75}$
(iii) $\left(\frac{3}{4}\right)^{2} \times\left(\frac{-1}{2}\right)^{3} \times 2^{3}$
Sol: $\frac{3 \times 3}{4 \times 4} \times-\frac{1 \times 1 \times 1}{2 \times 2 \times 2} \times 2 \times 2 \times 2$
$=\frac{-9}{16}$
(iv) $2^{2}+3^{3}+4^{3}$
Sol: $4+27+64$
=95 Ans
Q6 | Ex-5A |Class 7 | Exponents & Powers | S.Chand | Composite Mathematics | Chapter 5 | myhelper
Question 6
Write the following number as a power of 5 :
(i) 5
Sol: $5^{1}$
(ii) 25
Sol: $5^{2}$
(iv) 3125
Sol: $5^{5}$
(v) 625
Sol: $5^{4}$
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