Final answer:
The expression equivalent to 1/16 is 4⁻¹ x 4³. This result is found by adding the exponents when multiplying powers with the same base of 4, which should add up to -4, as 4⁻⁴ equals 1/16.
Step-by-step explanation:
The expression equivalent to 1/16 is 4⁻¹ x 4³. When we deal with exponents and multiplication, remember that when we multiply powers with the same base, we add the exponents. So, to find the expression equivalent to 1/16, we need two exponents that add up to -4, since 4⁻⁴ = 1/4⁴ = 1/16.
Now let's evaluate each option:
- 4¹ x 4⁻³ = 4⁽¹⁻³⁾ = 4⁻² = 1/4² = 1/16 but this is incorrect because 1/16 is equal to 4⁻⁴, not 4⁻².
- 4¹ x 4⁻¹⁰ = 4⁽¹⁻¹⁰⁾ = 4⁻⁹, which is not equal to 1/16.
- 4¹ x 4⁻⁴ = 4⁽¹⁻⁴⁾ = 4⁻³, which is not equal to 1/16.
- 4⁻¹ x 4³ = 4⁽⁻¹⁺³⁾ = 4², which indeed simplifies to 1/16.
Hence, the correct expression is 4⁻¹ x 4³.