Question

What is the value of a if 25ᵅ÷5³=5⁷

Answer 1

Step-by-step explanation:

==> 5^3×5^7×5^12

==> (By the exponential property)

==> 5^(3+7+12)

==> 5^22

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Answer 2

$\huge\purple {\underline {\underline{\tt{Solution:-}}}}$

${25}^{a} \div {5}^{3} = {5}^{7}$

$⟾\:( {5}^{2})^{a} \div {5}^{3} = {5}^{7}$

$⟾\:5^{2a} \div {5}^{3} = {5}^{7}$

$⟾ \: 5^{2a - 3} = {5}^{7}$

$⟾ \: 2a - 3 = 7$

$⟾ \: 2a = 7 + 3$

$⟾ \: 2a = 10$

$⟾ \: a = \frac{10}{2}$

$⟾ \: a = 5$

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Correction Test

$Left \: \: Side = 25^{5} \div {5}^{3}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9765625 \div 125$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 78125$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 5^{7}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = Right \: \: Side$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [Hence\:Proved]$

$\bold\green{\boxed{Hence,\:the\:value\:of\:a\:is\:5}}$

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