Question

Select all terms that are equivalent to 4³/4⁵

A. 4²
B. 1/16
C. 1/4²
D. -4²
E. 4^-²

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify 4³/4⁵, we can subtract the exponents because we have the same base.

4³/4⁵ = 4^(3-5) = 4^(-2)

Therefore, the term 4³/4⁵ is equivalent to 4^(-2).

The equivalent terms are:
E. 4^-²

Answer 2

[AI-generated answer — Step-by-Step Bot]

To simplify the expression 4³/4⁵, we can subtract the exponents in the denominator from the exponents in the numerator since the base is the same.

The expression 4³ can also be written as 4 * 4 * 4, which is equal to 64.
The expression 4⁵ can be written as 4 * 4 * 4 * 4 * 4, which is equal to 1024.

Now, we can rewrite the expression 4³/4⁵ as 64/1024.

To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 32.

64/1024 divided by 32/32 equals 2/32.

Since 2 and 32 have a common factor of 2, we can further simplify the fraction.

2/32 divided by 2/2 equals 1/16.

Therefore, the expression 4³/4⁵ is equivalent to 1/16.

So, the answer is B. 1/16.

Answer 3

[AI-generated answer — Explain Bot]

To find the equivalent terms for the expression 4³/4⁵, we can simplify the expression by using exponent rules. The rule states that dividing two numbers with the same base is equivalent to subtracting their exponents.

Given that the base is 4, we can subtract the exponents:
4³/4⁵ = 4^(3-5) = 4^-2

Therefore, the answer is E. 4^-².