If 5 sqrt{5} times 5^{3} div 5^{-frac{3}{2}} | vedclass

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(A) Given the expression: $5 \sqrt{5} 	imes 5^{3} \div 5^{-\frac{3}{2}} = 5^{a+2}$Express all terms with base $5$:$5^1 	imes 5^{1/2} 	imes 5^3 \div

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$4$

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(A) Given the expression: $5 \sqrt{5} 	imes 5^{3} \div 5^{-\frac{3}{2}} = 5^{a+2}$Express all terms with base $5$:$5^1 	imes 5^{1/2} 	imes 5^3 \div 5^{-3/2} = 5^{a+2}$Using the laws of exponents $x^m 	imes x^n = x^{m+n}$ and $x^m \div x^n = x^{m-n}$:$5^{(1 + 1/2 + 3 - (-3/2))} = 5^{a+2}$Simplify the exponent:$1 + 0.5 + 3 + 1.5 = 6$So,$5^6 = 5^{a+2}$Equating the exponents:$6 = a + 2$$a = 6 - 2 = 4$

If $5 \sqrt{5} \times 5^{3} \div 5^{-\frac{3}{2}} = 5^{a+2},$ then the value of $a$ is

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