Question

Evaluate (3/2)⁶×(3/2)⁴​

Answer 1

$\implies{ (\dfrac{3}{2})}^{6} \times { (\dfrac{3}{2})}^{4}$

We know that :

$\underline{ \boxed{ \bf {(a)}^{b} \times {(a)}^{c} = {(a)}^{b + c} }}$

Therefore :-

$\implies{ (\dfrac{3}{2})}^{6} \times { (\dfrac{3}{2})}^{4} = \bf {(\dfrac{3}{2})}^{6 + 4}$

$\implies{ (\dfrac{3}{2})}^{6} \times { (\dfrac{3}{2})}^{4} = {(\dfrac{3}{2})}^{10}$

We know that :-

$\underline{ \boxed{ \bf ({\dfrac{a}{b} ) }^{c} = \dfrac{ {(a)}^{c} }{ {(b)}^{c} } }}$

$\implies \sf {\dfrac{ {(3)}^{10} }{ {(2)}^{10} }}$

Answer:

$\sf {\dfrac{ {(3)}^{10} }{ {(2)}^{10} }} \: or \: {(\dfrac{3}{2})}^{10}$

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$\underline {\bf \red {learn \: more } } :$

$1)a^m \times a^n= {a}^{(m + n)}$

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

$3) {ab}^{n} = {a}^{n} {b}^{n}$

$4) \frac{ {(a)}^{m} }{ {(a)}^{n} } = {a}^{m - n}$

$5) {a}^{ - b} = \frac{1}{ {a}^{b} }$