Apply All Exponent Rules Quick Check3 of 53 of 5 ItemsQuestionWhich 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)Responses172 ⋅ (−4)−3Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction(−4)372start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction72(−4)3Start Fraction 7 squared over left parenthesis negative 4 right parenthesis cubed end fraction4372
To simplify the expression and convert the exponents to positive, we can use the properties of integer exponents:
150 ⋅ 7^-2 (-4)^-3
First, let's deal with the negative exponents:
7^-2 = 1/7^2 = 1/49
(-4)^-3 = 1/(-4)^3 = 1/(-64) = -1/64
Now, substitute these values back into the expression:
150 ⋅ (1/49) ⋅ (-1/64)
Next, simplify the expression:
150/1 ⋅ 1/49 ⋅ (-1/64) = (150 ⋅ -1)/(1 ⋅ 49 ⋅ 64) = -150/3136
So, the equivalent expression with only positive exponents is -150/3136.
The correct answer is:
72(−4)3