What is the value of 0.2 all to the
power of negative three?
Well, if we think about 0.2, what
the 0.2 is is the same as two-tenths. And that’s because if we look at
the place values, our zero is the units and our two is the tenths. So, we’re gonna say that 0.2 is
equal to two-tenths. But can we make this any
simpler? Well, yes, we can simplify the
fraction by dividing the numerator and denominator by two. And when we do this, what we get is
one over five or one-fifth because two divided by two is one and 10 divided by two
is five. So, we know that 0.2 is equal to a
fifth. And in fact, this is a decimal
conversion that we should know.
So, what we’re gonna get is
one-fifth to the power of negative three. Well, if we recall that we got 𝑥
to the power of negative 𝑛 equals one over 𝑥 to the power of 𝑛, it’s slightly
different here because we’ve got a fraction, one over five. But it’s exactly the same theory
because what we’re going to do is we’re going to find the reciprocal of one over
five. And then we’re gonna put it to the
power of three.
So, we can think of it as five
cubed over one cubed. And that’s because the reciprocal
of one over five is five over one. But usually, we wouldn’t bother
writing the one cubed on the denominator. Well, five cubed means five
multiplied by five multiplied by five. Well, five multiplied by five is
25, and 25 multiplied by five is 125. So therefore, we can say that the
value of 0.2 to the power of negative three is 125.