Ask a New Question
Menu

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

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
11 months ago

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