Find the value of negative one-half
squared multiplied by one over two squared squared.
The expression we’ve been asked to
find the value of is the product of two terms, each of which is a power of a
fractional value. The exponents for both terms are
the same. And so we can apply one of the laws
of exponents in reverse to simplify this product.
When we have a product of two
rational numbers 𝑎 and 𝑏 raised to a power 𝑚, this is equivalent to raising each
factor separately to the power of 𝑚 and then finding the product. So applying this law the other way
round, we can say that if we are squaring each of the fractions and then finding
their product, that’s the same as finding the product of the fractions and then
squaring the result.
We can then simplify the value
inside the parentheses. First, we evaluate two squared,
which is four. Then, we multiply the fractions by
multiplying the numerators and multiplying the denominators to give negative
We can evaluate this in two
ways. First, we could just multiply
negative one-eighth by itself, recalling the usual rules for multiplying fractions,
to give one over 64. Alternatively, we can recall
another law of exponents, which is that when we raise a fraction with a nonzero
denominator to a power, this is equivalent to raising the numerator and denominator
separately to that power. So negative one over eight squared
is equal to negative one squared over eight squared, which is one over 64.
So, using laws of exponents, we’ve
found that the value of negative one-half squared multiplied by one over two squared
squared is one over 64.