Question

Which expression is equivalent to (4^3)/(4^-3)?

a) 4^5
b) 4^6
c) 4^-1
d) 4^-6

Answer 1

The expression (4^3)/(4^-3) simplifies to 4^6, by applying the property of exponents which states that when dividing like bases, you subtract the exponents. This yields 4^(3 - (-3)) = 4^6.

Step-by-step explanation:

The expression (4^3)/(4^-3) can be simplified using the properties of exponents. When dividing powers with the same base, you subtract the exponents. Therefore, the exponent in the numerator, which is 3, is subtracted from the exponent in the denominator, which is -3. So we get 4^(3 - (-3)) = 4^6.

The calculation steps are as follows:

1. Identify the base which is 4.
2. Subtract the exponent in the denominator from the exponent in the numerator: 3 - (-3) = 3 + 3 = 6.
3. Write the result as a single exponent: 4^6.

Thus, the equivalent expression to (4^3)/(4^-3) is 4^6, which corresponds to option b).