Express each of the following as a product of powers of their prime…

Question 2 of 28intermediate🔧 ApplyNumerical4 marks

Express each of the following as a product of powers of their prime factors in exponential form. (i) $648$ (ii) $405$ (iii) $540$ (iv) $3600$

(i)

Answer

$648 = 2^3 \times 3^4$

(ii)

Answer

$405 = 3^4 \times 5$

(iii)

Answer

$540 = 2^2 \times 3^3 \times 5$

(iv)

Answer

$3600 = 2^4 \times 3^2 \times 5^2$

Explanation

(i) Prime factorization: $648 = 8 \times 81 = 2^3 \times 3^4$ (ii) Prime factorization: $405 = 5 \times 81 = 5 \times 3^4 = 3^4 \times 5$ (iii) Prime factorization: $540 = 4 \times 135 = 2^2 \times 27 \times 5 = 2^2 \times 3^3 \times 5$ (iv) Prime factorization: $3600 = 36 \times 100 = 6^2 \times 10^2 = (2 \times 3)^2 \times (2 \times 5)^2 = 2^4 \times 3^2 \times 5^2$

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