Question

evaluate (25)⅓ × (5)⅓​

Answer 1

$\huge \bf \colorbox{red}{solution}$

==》To get these answers, you would have used the following laws of exponents, . (Here a, n and m are natural numbers. Remember, a is called the base and m and n are the exponents.)

$\bf \colorbox{cyan}{by \: using \: the \: law \:of \: exponent }$

==》Let a > 0 be a real number and m and n be rational numbers then ;-

${a}^{m} {b}^{m} = ( {ab})^{m}$

$(25) ^{ \frac{1}{3} } \times (5) ^{ \frac{1}{3} } \\ \\ = (25 \times 5) ^{ \frac{1}{3} } \\ \\ = ( {5}^{3}) ^{ \frac{1}{3} } \\ \\ = > = 5$

$\bf \colorbox{yellow}{laws \: of \: exponents \: of \: real \: numbers}$

➡️Let a > 0 be a real number and m and n be rational numbers then ;-

$(i) \: {a}^{m} . {a}^{n} = {a}^{m + n} \\ \\ (ii) \: \: \: ({a}^{m})^{n} = {a}^{mn} \\ \\ (iii) \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \\ \\ (iv) \: \: {a}^{m} {b}^{m} \: = \: (ab)^{m}$