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
72(−4)3
Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction
(−4)372
start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction
172 ⋅ (−4)−3
The correct answer is (a) 4372.
To simplify the expression and get rid of the negative exponents, we can apply the properties of integer exponents.
1. 150 ⋅ 7^-2 = 150 / 7^2 (by converting a negative exponent to a positive exponent by taking the reciprocal)
2. (-4)^-3 = 1 / (-4)^3 (by converting a negative exponent to a positive exponent by taking the reciprocal)
Now we can simplify further:
1. 150 / 7^2 = 150 / 49 (since 7^2 = 49)
2. 1 / (-4)^3 = 1 / (-4 * -4 * -4) = 1 / (-64) = -1/64
Finally, we can multiply the simplified expressions:
150 / 49 * -1/64 = (150 * -1) / (49 * 64) = -150 / 3136 = -75/1568
Therefore, the equivalent expression with only positive exponents is not one of the given options. The correct answer is -75/1568, which is not listed.