Class 7 Chapter 5 Ex 5A

 Exercise 5A 

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)  $x \times x \times x \times x \times d \times x \times x$ 

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: $3^{2} \times 11^{3}$

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: $-37 \times -37 \times 4 \times 4 \times 4 \times 4$

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) $\frac{-8}{2^{7}}=\frac{-2^{3}}{3^{3}}=\left(\frac{-2}{3}\right)^{3}$

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

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:   $5^{4}$