Question Video: Finding the Value of an Expression Using Laws of Exponents Mathematics • 8th Grade

Find the value of (−(1/2))² × (1/2²)².


Video Transcript

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 one-eighth squared.

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.

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