Video Transcript
Calculate two to the power of
negative two multiplied by three to the power of negative one all to the power of
negative one, giving your answer in its simplest form.
So, first of all, what we’re doing
is we’re gonna use our rule that we have — that’s 𝑥 to the power of negative 𝑛
equals one over 𝑥 to the power of 𝑛 — to convert our negative exponents into
factions. So, first of all, we’re gonna have
two to the power of negative two. And this’s gonna be equal to one
over two squared, which is gonna be equal to one over four. So, we can say that two to the
power of negative two is equal to a quarter. Then, next, what we have is three
to the power of negative one. And we know that three to the
negative one is gonna be equal to one over three. And that’s because it’s the
reciprocal of three over one. So, three over one is what three
is. Reciprocal of that is one over
three. Okay, great, we’ve converted them
both into fractions.
Okay, great, so, now, what we have
is a quarter multiplied by a third all to the power of negative one. Well, if we multiply a fraction,
what we do is we multiply the numerators then multiply the denominators. So, one multiplied by one is
one. Four multiplied by three is 12. So, we’ve got one over 12 or one
twelfth to the power of negative one. Well, as we said before, when we’ve
got something raised to the power of negative one, what we need to do is just find
the reciprocal. And to find the reciprocal, what
you do is you flip the numerator and denominator.
So therefore, our two to the power
of negative two multiplied by three to the power of negative one all to the power of
negative one becomes 12. And that’s because the final step
was to have one over 12, or one twelfth, to the power of negative one. Well, the reciprocal of one over 12
is just 12.
