Express each of the following numbers using the exponential notation:(i) 3125
(ii) 729
(iii) 343
(iv) 512
Given :
The given numbers are (i) 3125 (ii) 729 (iii) 343 (iv) 512.
To do :
We have to express the given numbers in exponential form.
Solution :
(i) 3125
$3125 = 5 \times 5\times 5\times 5 \times 5 = 5^5$
Therefore, 3125 in exponential form is $5^5$.
(ii) 729
$729 = 3 \times 3\times 3\times 3 \times 3 = 3^5$
Therefore, 729 in exponential form is $3^5$.
(iii) 343
$343 = 7 \times 7\times 7 = 7^3$
Therefore, 343 in exponential form is $7^3$.
(iv) 512
$512 = 8 \times 8\times 8 = 8^3$
Therefore, 512 in exponential form is $8^3$.
Related Articles
- Express each of the following numbers using the exponential notation:$(i)$ 512$(ii)$ 343$(iii)$ 729$(iv)$ 3125
- Express each of the following numbers in exponential form:\n\n(1) 512 (2)625 (3)729
- Express each of the following as a product of prime factors only in exponential form:$(i)$. $108\times192$$(ii)$. $270$$(iii)$. $729\times64$$(iv)$. $768$
- Show that:(i) \( \frac{\sqrt[3]{729}}{\sqrt[3]{1000}}=\sqrt[3]{\frac{729}{1000}} \)(ii) \( \frac{\sqrt[3]{-512}}{\sqrt[3]{343}}=\sqrt[3]{\frac{-512}{343}} \)
- Find the cube root of each of the following numbers:(i) $8 \times 125$(ii) $-1728 \times 216$(iii) $-27 \times 2744$(iv) $-729 \times -15625$
- Express each in exponential form.(i) 1296(ii) 576
- Find the cube root of the numbers: $2460375,20346417,210644875,57066625$ using the fact that(i) $2460375 = 3375 \times 729$(ii) $20346417 = 9261 \times 2197$(iii) $210644875 = 42875 \times 4913$(iv) $57066625 = 166375 \times 343$
- Find the squares of the following numbers(i) 425(ii) 575(iii) 405(iv) 205(v) 95(vi) 745(vii) 512(viii) 995.
- Find the cube root of each of the following rational numbers:(i) $0.001728$(ii) $0.003375$(iii) $0.001$(iv) $1.331$
- Express the following numbers in standard form:$(i)$. $5,00,00,000$ $(ii)$. $70,00,000$ $(iii)$. $3,18,65,00,000$$(iv)$. $3,90,878$ $(v)$. $39087.8$ $(vi)$ $3908.78$
- Find the cube root of each of the following rational numbers.(i) \( \frac{-125}{729} \)(ii) \( \frac{10648}{12167} \)(iii) \( \frac{-19683}{24389} \)(iv) \( \frac{686}{-3456} \)(v) \( \frac{-39304}{-42875} \)
- Express each of the following numbers in exponential form:(1) 125 (2)243 (3)288
- Using prime factorization method, find which of the following numbers are perfect squares?(i) 189(ii) 225(iii) 2048(iv) 343(v) 441(vi) 2916(vii) 11025(viii) 3549
- Find the squares of the following numbers using diagonal method:(i) 98(ii) 273(iii) 273(iv) 295(v) 171
- Find the squares of the following numbers:(i) 127(ii) 503(iii) 451(iv) 862(v) 265.
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies