Question

Which expressions are equivalent to (4^3)⋅(4^−6)?

Select each correct answer.
a. 4³
b. −64
c. 1/64
d.−1/64
e. 64
f. 1/4^3
g.4^−3

Answer 1

To find the equivalent expressions to (4^3)⋅(4^−6), we need to simplify the expression using the properties of exponents. The expression is equivalent to 1/4^3.

Step-by-step explanation:

To find the equivalent expressions to (4^3)⋅(4^−6), we need to simplify the expression using the properties of exponents. In this case, we can use the rule that states when multiplying two numbers with the same base, we add the exponents. So, (4^3)⋅(4^−6) can be rewritten as 4^(3+(-6)). Simplifying the exponent, we get 4^(-3). This means that the expression is equivalent to 1/4^3, which is option f.

To verify this, let's evaluate both expressions: (4^3)⋅(4^−6) = 64⋅(1/64) = 1, while 1/4^3=1/64.

Therefore, the expressions equivalent to (4^3)⋅(4^−6) are options f: 1/4^3.