Find n 2 3 3 - 2 3 5 - 2 3 n-2

( 23)^3×( 23)^5 = ( 23)^n 2 ⇒( 23)^8 = ( 23)^n 2 ⇒ n 2 = 8 ⇒ n = 10 ...

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Byju's Answer

Standard VII

Mathematics

Exponents with Unlike Bases and Same Exponent

Find n 2 ...

Question

Find $n$
${(\frac{2}{3})}^{3} \times {(\frac{2}{3})}^{5} = {(\frac{2}{3})}^{n - 2}$

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Solution

${(\frac{2}{3})}^{3} \times {(\frac{2}{3})}^{5} = {(\frac{2}{3})}^{n - 2}$
$\Rightarrow {(\frac{2}{3})}^{8} = {(\frac{2}{3})}^{n - 2}$
$\Rightarrow n - 2 = 8$
$\Rightarrow n = 10$

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Find n(23)3×(23)5=(23)n−2

(23)3×(23)5=(23)n−2⇒(23)8=(23)n−2⇒n−2=8⇒n=10

Find $n$
${(\frac{2}{3})}^{3} \times {(\frac{2}{3})}^{5} = {(\frac{2}{3})}^{n - 2}$

${(\frac{2}{3})}^{3} \times {(\frac{2}{3})}^{5} = {(\frac{2}{3})}^{n - 2}$
$\Rightarrow {(\frac{2}{3})}^{8} = {(\frac{2}{3})}^{n - 2}$
$\Rightarrow n - 2 = 8$
$\Rightarrow n = 10$