Question

Would the following expression create a fraction? Explain why or why not. 2^-5 x 2^3

a) Yes, because negative exponents indicate fractions.
b) No, because the bases are different.
c) Yes, because the bases are the same.
d) No, because the exponents are too small.

Answer 1

The expression 2⁻⁵ x 2³ creates a fraction, specifically 1/4.

Step-by-step explanation:

The given expression is 2⁻⁵ x 2³. To determine if it creates a fraction, we need to simplify the expression. Using the property of exponents that states am x an = am+n, we can combine the exponents. So, 2⁻⁵ x 2³ becomes 2⁻⁵⁺³ = 2⁻². A negative exponent represents the reciprocal of the base raised to the positive exponent. Therefore, 2⁻² can be written as 1/2² = 1/4. Hence, the expression creates a fraction, specifically 1/4. This manipulation illustrates how negative exponents transform into reciprocals, culminating in a fractional form, indicating that the expression equates to 1/4.