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Powers with Positive and Negative Exponents

If 5 / 2 2...

Question

If ${(\frac{5}{2})}^{2} \times {(\frac{5}{2})}^{a + 5} = {(\frac{5}{2})}^{8}$ , then find 'a' -

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Solution

${(\frac{5}{2})}^{2} \times {(\frac{5}{2})}^{a + 5} = {(\frac{5}{2})}^{8} {(\frac{5}{2})}^{2 + a + 5} = {(\frac{5}{2})}^{8}$
Comparing powers
$a + 7 = 8 a = 1$

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{(\frac{3}{2})}^{2} \times {(\frac{3}{2})}^{a + 5} = {(\frac{3}{2})}^{8}

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{(\frac{3}{2})}^{2} \times {(\frac{3}{2})}^{a + 5} = {(\frac{3}{2})}^{8}

, then the value of

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