Question

by what number should (3) to the power -8 be multiplied to get (3) to the power -4​

Answer 1

Question :

$By \: what \: number \: should \: {3}^{ - 8} \: be \: \\ multiplied \:\: to \: get \: {3}^{ - 4}$

Solution :

Let the number be X.

According to the question :-

$\implies \: {3}^{ - 8} \times x ={3}^{ - 4}$

$\implies \: x = \dfrac{{(3)}^{ - 4} }{{(3)}^{ - 8}}$

we know that :-

$\dfrac{{(a)}^{ b} }{{(a)}^{ c}} = {(a)}^{ b - c}$

$\implies \: x ={3}^{ - 4 - ( - 8)}$

$\implies \: x ={3}^{ - 4 + 8}$

$\implies \: x ={3}^{ 4}$

$\implies \: x ={3} \times 3 \times 3 \times 3$

$\implies \: x =81$

Answer : 81

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Learn more:

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

$2) {( {a}^{m})}^{n}  = {a}^{mn}$

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

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

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