Question

Select all the expressions that are equivalent to 4⁸*4⁻⁵
a. 4³
b. 4⁶/4⁹
c. (4⁸)⁻⁵

Answer 1

Only option a. 4³ is equivalent to 4⁸*4⁻⁵. We use the laws of exponents to add the exponents when the bases are the same, leading to 4³ as the simplified form.

Step-by-step explanation:

The question asks to select all expressions that are equivalent to 4⁸*4⁻⁵. First, we need to apply the laws of exponents, which state that when multiplying powers with the same base, we add the exponents. Thus, 4⁸*4⁻⁵ becomes 4³, because 8 - 5 = 3.

Now, let's look at the options:

1. a. 4³: This is the correct answer as we just calculated above.
2. b. 4⁶/4⁹: This expression simplifies to 4⁻³ (not equivalent to 4³).
3. c. (4⁸)⁻⁵: This expression suggests an inverse operation, which is not equivalent to 4³.

Therefore, the correct expression that is equivalent to 4⁸*4⁻⁵ is a. 4³.

The expression 4⁸ * 4⁻⁵ can be simplified using the rule of power of powers, which states that when you multiply two powers with the same base, you add the exponents. Therefore, 4⁸ * 4⁻⁵ becomes 4^(8 + (-5)).

Adding the exponents, we get 4³, which is equivalent to option a.

Therefore, option a is the expression that is equivalent to 4⁸ * 4⁻⁵.