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Express each of the following as a product of prime factors only in exponential form: (i) \({108}\times{192}\) (ii) \({1270}\) (iii) \({729}\times{64}\) (iv) \({768}\)
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Question

Express each of the following as a product of prime factors only in exponential form: (i) \({108}\times{192}\) (ii) \({1270}\) (iii) \({729}\times{64}\) (iv) \({768}\)

Answer

(i)\({2}^{8}\times {3}^{4}\),( ii) \(2\times 5\times 127\) ,(iii)\({2}^{6}\times {3}^{6}\), (iv)\({2}^{8}\times 3\)
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Solution

i) 108×192
Solution for Express each of the following as a product of prime factors only in exponential form: (i) {108}times{192} (ii) {1270} (iii) {729}times{64} (iv) {768}
\({108}={2}^{{2}}\times{3}^{{3}}\)
\({192}={2}^{{6}}\times{3}\)
So,\(108×192=2^8×3^4\ \ \\ [a^m\times a^n=a^{m+n}]\)
ii)1270
Solution for Express each of the following as a product of prime factors only in exponential form: (i) {108}times{192} (ii) {1270} (iii) {729}times{64} (iv) {768}
So, \(1270 = 2\times5\times127 \)
iii) \({729}\times{64}\)
Solution for Express each of the following as a product of prime factors only in exponential form: (i) {108}times{192} (ii) {1270} (iii) {729}times{64} (iv) {768}
\(729= 3^6\)
\(64=2^6\)
So, \({729}\times{64}=2^6\times 3^6\)
iv)  \({768}\)
Solution for Express each of the following as a product of prime factors only in exponential form: (i) {108}times{192} (ii) {1270} (iii) {729}times{64} (iv) {768}
So, \(768=2^8\times3\)
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