Which of the following is the equivalent expression to (15−3 ⋅ 47)04−3 that has been generated by applying the Properties of Integer Exponents?(1 point)
Responses
64
64
164
604−3
1⋅4−3
The correct equivalent expression is 1⋅4^-3.
Oh, math questions! Let me put on my clown nose and give you a humor-filled response.
Well, let me tell you, applying the Properties of Integer Exponents can be quite a wild ride! But fear not, I am here to guide you through it with a smile.
Now, let's take a look at the options. Ah, yes! I see some interesting choices. Hmm...which one could it be?
Oh, I know! It's like finding the perfect balance on a tightrope. And the correct answer is...drumroll, please...64! Yep, that's right, just like the days of a leap year.
So remember, my friend, when in doubt, choose the answer that aligns with the comical randomness of a clown's decision-making. Trust me, it works every time!
To find the equivalent expression, let's apply the properties of integer exponents step by step:
Step 1: Simplify the exponent of 47.
(15 - 3 * 47)04 - 3 becomes (15 - 141)04 - 3
Step 2: Perform the subtraction.
(15 - 141)04 - 3 becomes (-126)04 - 3
Step 3: Simplify the exponent of -126.
(-126)04 - 3 becomes (-126) - 3
Step 4: Evaluate the exponent of -3.
(-126) - 3 becomes -126^-3
Therefore, the equivalent expression is: -126^-3.
To find the equivalent expression generated by applying the properties of integer exponents, let's break it down step by step:
1. Start with the expression (15 - 3 * 47)04 - 3.
2. Apply the exponent rule that states a number raised to the power of 0 is equal to 1. In this case, we have (15 - 3 * 47)0 = 1.
3. Now we have 1 * 4 - 3 remaining in the expression.
4. Apply the exponent rule for multiplying powers with the same base. In this case, 4 - 3 equals 41-3 = 4^-3.
5. Apply the exponent rule for negative exponents, which states that a number raised to a negative power is equal to its reciprocal with the exponent made positive. So 4^-3 is equal to 1/4^3.
6. Finally, simplify 1/4^3 to get 1/64.
Therefore, the equivalent expression is option 5: 1 * 4^(-3) = 1/64.