Question 176825
{{{(1/8)^(-2t)=2^(t+3)}}} Start with the given equation.



{{{(2^(-3))^(-2t)=2^(t+3)}}} Rewrite {{{1/8}}} as {{{1/8=8^(-1)=(2^3)^(-1)=2^(-3)}}}



{{{2^(6t)=2^(t+3)}}} Multiply the exponents.



Since the bases are equal, the exponents are equal.



{{{6t=t+3}}} Set the exponents equal to one another.



{{{6t-t=3}}} Subtract {{{t}}} from both sides.



{{{5t=3}}} Combine like terms on the left side.



{{{t=(3)/(5)}}} Divide both sides by {{{5}}} to isolate {{{t}}}.



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Answer:


So the answer is {{{t=3/5}}}