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

172 ⋅ (−4)−3
Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline 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

72(−4)3

Answer 1

I’m not sure how to read the original expression — please confirm whether it is
- 150 · 7^(−2) · (−4)^(−3) (i.e. 150 times 7^(−2) times (−4)^(−3)), or
- something else (type exponents with ^, e.g. 150*7^-2*(-4)^-3).

If it is 150 · 7^(−2) · (−4)^(−3), moving the negative exponents to the denominator gives an expression with only positive exponents:
150/(7^2 · (−4)^3).
You can simplify numerically: (−4)^3 = −64, so 150/(7^2 · (−64)) = 150/(49·(−64)) = 150/(−3136) = −75/1568.

If instead the expression was 1/(7^(−2) (−4)^(−3)) then it equals (−4)^3 / 7^2.

Tell me which original you meant and I’ll pick the matching choice from your list.