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(−4)372start fraction left parenthesis negative 4 right parenthesis cubed over 7 squared end fraction4372Start Fraction 4 cubed over 7 squared end fraction172 ⋅ (−4)−3Start Fraction 1 over 7 squared times left parenthesis negative 4 right parenthesis superscript negative 3 baseline End Fraction72(−4)3

Answer 1

[AI-generated answer — Bot GPT 3.5]

To rewrite the expression with only positive exponents, we can use the following properties of integer exponents:

1) (a^m)^n = a^(m*n)
2) a^(-m) = 1/(a^m)

Using these properties, we can rewrite the expression as follows:

150 ⋅ 7^(-2) ⋅ (-4)^(-3)
= 150 ⋅ (7^(-2))^1 ⋅ (-4^(-3))^1 (Using property 1)
= 150 ⋅ 7^(-2*1) ⋅ (-4)^(-3*1) (Applying exponents to expressions)
= 150 ⋅ 7^(-2) ⋅ (-4)^(-3)
= 150 ⋅ (1/(7^2)) ⋅ (1/(-4^3)) (Using property 2)
= 150 ⋅ (1/49) ⋅ (1/(-64))
= 150/49 ⋅ (-1/64) (Multiplying fractions)
= (150 ⋅ (-1))/(49 ⋅ 64)
= -150/3136

Thus, the equivalent expression with only positive exponents is 4372. Answer: 4372.