Maths / Exponents and Power / Statement Sums Involving Exponent and Power

QUESTION

If  $\dpi{120} \fn_jvn \large 4^x+4^x+4^x+4^x+4^x+4^x+4^x+4^x=\frac {1}{512}, \; then$  what is the value of  $\dpi{120} \fn_jvn \large \frac {-3}{x}?$

EXPLANATION
Explain TypeExplanation Content
Text

$4^x+4^x+4^x+4^x+4^x+4^x+4^x+4^x=\frac {1}{512}$

$8(4^x)=\frac {1}{512}$

$4^x=\frac {1}{512 \times 8}$

$4^x=(512 \times 8)^-^1$

$4^x=4^-^6$

$\therefore \; \; x=-6$

$\Rightarrow \frac {-3}{x}=\frac {-3}{-6}=\frac {1}{2}=0.50$

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