Question

n= 3 times 5 squared times x squared

express 5n squared as a product of prime factors in index form

please help

Answer 1

$n = 3\times 5^{2} \times x^{2} \: (given)$

$5n^{2} = 5 \times ( 3\times 5^{2} \times x^{2})^{2}\\= 5 \times 3^{2} \times (5^{2})^{2} \times (x^{2})^{2}$

$\boxed { \pink { (ab)^{n} = a^{n} \times b^{n} }}$

$= 5 \times 3^{2} \times 5^{4}\times x^{4}$

$\boxed { \pink { (a^{m})^{n} = a^{m \times n} }}$

$= 3^{2} \times 5^{1+4}\times x^{4}$

$\boxed { \pink { a^{m} \times a^{n} = a^{m+n} }}$

$= 3^{2} \times 5^{5}\times x^{4}$

Therefore.,

$\red {5n^{2}}\green {= 3^{2} \times 5^{5}\times x^{4}}$

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