Apply All Exponent Rules Quick Check
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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
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
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
172 ⋅ (−4)−3
The correct answer is 72(−4)3.
To simplify the expression 150 ⋅ 7^(-2) ⋅ (-4)^(-3) and generate an equivalent expression with only positive exponents, we can apply the properties of integer exponents as follows:
1. Start by simplifying the expressions with negative exponents:
7^(-2) = 1/(7^2) = 1/49
(-4)^(-3) = 1/((-4)^3) = 1/(-64) = -1/64
2. Substitute the simplified expressions back into the original expression:
150 ⋅ 1/49 ⋅ -1/64
3. To multiply fractions, we can multiply the numerators together and the denominators together:
(150 ⋅ -1) / (49 ⋅ 64)
4. Multiply the numerators and the denominators:
-150 / 3136
Therefore, an equivalent expression to 150 ⋅ 7^(-2) ⋅ (-4)^(-3) with only positive exponents is -150/3136.