If 55–√×53÷5−32 = 5a+2,then the value of a is = ?If 55×53÷5−32 = 5a+2,then the value of a is = ?\eqalign{ & {\text{If 5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}{\text{,}} \cr & {\text{then the value of }}a{\text{ is = ?}} \cr} " /> If 55–√×53÷5−32 = 5a+2,then the value of a is = ?If 55×53÷5−32 = 5a+2,then the value of a is = ?\eqalign{ & {\text{If 5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}{\text{,}} \cr & {\text{then the value of }}a{\text{ is = ?}} \cr} " /> If 55–√×53÷5−32 = 5a+2,then the value of a is = ?If 55×53÷5−32 = 5a+2,then the value of a is = ?\eqalign{ & {\text{If 5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}{\text{,}} \cr & {\text{then the value of }}a{\text{ is = ?}} \cr} " />

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$\begin{aligned} If 5 \sqrt{5} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2}, \\ then the value of a is = ? \end{aligned}$ $\eqalign{ & {\text{If 5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}{\text{,}} \cr & {\text{then the value of }}a{\text{ is = ?}} \cr}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} 5 \sqrt{5} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1} \times 5^{\frac{1}{2}} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 - (- \frac{3}{2})} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 + \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{6} = 5^{a + 2} \\ \Rightarrow a + 2 = 6 \\ \Rightarrow a = 4 \end{aligned}

$\eqalign{ & {\text{5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {{\text{5}}^1} \times {5^{\frac{1}{2}}} \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 - \left( { - \frac{3}{2}} \right)}} = {5^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 + \frac{3}{2}}} = {5^{a + 2}} \cr & \Rightarrow {5^6} = {5^{a + 2}} \cr & \Rightarrow a + 2 = 6 \cr & \Rightarrow a = 4 \cr}$

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", "text": "

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

$\eqalign{ & {\text{If 5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}}{\text{,}} \cr & {\text{then the value of }}a{\text{ is = ?}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} 5 \sqrt{5} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1} \times 5^{\frac{1}{2}} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 - (- \frac{3}{2})} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 + \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{6} = 5^{a + 2} \\ \Rightarrow a + 2 = 6 \\ \Rightarrow a = 4 \end{aligned}

$\eqalign{ & {\text{5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {{\text{5}}^1} \times {5^{\frac{1}{2}}} \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 - \left( { - \frac{3}{2}} \right)}} = {5^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 + \frac{3}{2}}} = {5^{a + 2}} \cr & \Rightarrow {5^6} = {5^{a + 2}} \cr & \Rightarrow a + 2 = 6 \cr & \Rightarrow a = 4 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} 5 \sqrt{5} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1} \times 5^{\frac{1}{2}} \times 5^{3} \div 5^{- \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 - (- \frac{3}{2})} = 5^{a + 2} \\ \Rightarrow 5^{1 + \frac{1}{2} + 3 + \frac{3}{2}} = 5^{a + 2} \\ \Rightarrow 5^{6} = 5^{a + 2} \\ \Rightarrow a + 2 = 6 \\ \Rightarrow a = 4 \end{aligned}

$\eqalign{ & {\text{5}}\sqrt 5 \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {{\text{5}}^1} \times {5^{\frac{1}{2}}} \times {{\text{5}}^3} \div {{\text{5}}^{ - \frac{3}{2}}}{\text{ = }}{{\text{5}}^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 - \left( { - \frac{3}{2}} \right)}} = {5^{a + 2}} \cr & \Rightarrow {5^{1 + \frac{1}{2} + 3 + \frac{3}{2}}} = {5^{a + 2}} \cr & \Rightarrow {5^6} = {5^{a + 2}} \cr & \Rightarrow a + 2 = 6 \cr & \Rightarrow a = 4 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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