Which of the following is an equivalent expression to 150 ⋅ 7−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Question

Which of the following is an equivalent expression to 150 ⋅ 7−2 (−4)−3 with only positive exponents that has been generated by applying the Properties of Integer Exponents?(1 point)

Responses

72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction

4372
Start Fraction 4 cubed over 7 squared end fraction

(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction

172 ⋅ (−4)−3

Answer 1

The correct equivalent expression with only positive exponents is (−4)372.

Answer 2

To find the equivalent expression with only positive exponents, we can apply the Properties of Integer Exponents.

Let's break down the steps:

Step 1: Simplify 7^(-2):
Using the property a^(-n) = 1 / (a^n), we can rewrite 7^(-2) as 1 / (7^2).
So, 7^(-2) = 1 / 49.

Step 2: Simplify (-4)^(-3):
Similarly, applying the property a^(-n) = 1 / (a^n), we can rewrite (-4)^(-3) as 1 / ((-4)^3).
So, (-4)^(-3) = 1 / (-4)^3.
This can also be written as 1 / (-64).

Step 3: Simplify the expression:
Now, substitute the simplified values from Step 1 and Step 2 into the original expression:

150 * (7^(-2)) * ((-4)^(-3))

Substituting 7^(-2) = 1/49 and (-4)^(-3) = 1/(-64):

150 * (1/49) * (1/(-64))

We can simplify this expression further by multiplying the numbers:

(150 * 1 * 1) / (49 * (-64))

Multiplying the numbers, we get:

150 / (-3136)

Finally, simplifying this fraction, we have:

-150/3136

Therefore, the equivalent expression with only positive exponents is (-150/3136).

Answer 3

To find an equivalent expression with only positive exponents, we can apply the properties of integer exponents.

Starting with the given expression: 150 ⋅ 7^(-2) * (-4)^(-3)

First, we can simplify the negative exponents by applying the property that states a^(-n) = 1 / (a^n).

So, 7^(-2) can be rewritten as 1 / (7^2) and (-4)^(-3) can be rewritten as 1 / ((-4)^3).

Now we have: 150 * (1 / (7^2)) * (1 / ((-4)^3))

Next, we can apply another property of exponents that states (a/b)^n = (a^n) / (b^n).

So, (1 / (7^2)) can be rewritten as (7^(-2)) and (1 / ((-4)^3)) can be rewritten as ((-4)^(-3)).

Now we have: 150 * (7^(-2)) * ((-4)^(-3))

Finally, we can rearrange the terms to get an equivalent expression with positive exponents.

The equivalent expression is: 150 * (7^(-2)) * ((-4)^(-3))

Therefore, the correct answer is (1 point) 150 * 7^(-2) * (-4)^(-3)