Question

which single power is a equivalent to the expression (4^3)^2/ 4^2 ?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (4^3)^2/4^2, we can follow the order of operations (PEMDAS/BODMAS) which states that exponents should be simplified before division.

(4^3)^2 means we raise 4 to the power of 3 first, so (4^3)^2 = 64^2 = 4096.

Then we have 4096/4^2. Since 4^2 is 16, we can substitute it into the expression:
4096/16 = 256.

Therefore, the equivalent single power to the expression (4^3)^2/4^2 is 256.

Answer 2

which single power is equivalent to the expression 7^5 x (7^4)^3

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression, we need to follow the order of operations and simplify the exponents first.

Recall that when you raise a power to another power, you multiply the exponents.

First, simplify the exponent of (7^4)^3:
(7^4)^3 = 7^(4*3) = 7^12.

Now, the expression becomes 7^5 x 7^12.

When multiplying powers with the same base, you add the exponents.
Thus, 7^5 x 7^12 = 7^(5+12) = 7^17.

Therefore, the equivalent single power to the expression 7^5 x (7^4)^3 is 7^17.

Answer 4

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

To simplify the expression (4^3)^2/4^2, we can apply the rules of exponents.

Step 1: Calculate the exponent of (4^3)^2.
(4^3)^2 = 4^(3*2) = 4^6

Step 2: Calculate the exponent of 4^2.
4^2 = 16

Step 3: Divide (4^6) by 16.
(4^6)/16 = 4096/16 = 256

Therefore, the expression (4^3)^2/4^2 is equivalent to the single power 256.