In Exercises 85–116, simplify each exponential expression.(2a⁵)(-...

Question

In Exercises 85–116, simplify each exponential expression.(2a⁵)(-3a⁻⁷)

Accepted Answer

Hello, everyone. We are going to simplify the following expression and write the answer with positive exponents. Our expression is open parentheses. Six C cubed closed parentheses multiplied by open parentheses. Negative seven C raised to the negative 13th power closed parentheses. Our answer choices are a negative 42 divided by C raised to the 39th power B negative 42 C raised the 16th power C -42 divided by C raised to the 10th power D - C raised to the 10th power I know because I have two sets of parentheses directly next to each other that these are multiplied. So I'm rewriting my parentheses. I have open parentheses. Six C cubed closed parentheses multiplied by negative seven C. Raise the negative 13th power closed parentheses. When I simplify expressions with coefficients, I'm gonna multiply my coefficients just like I would if there were no variables. So six multiplied by -7 is -42. Next, I'm going to multiply my variables. And I recall that when I multiply like bases, I add the exponents. So the base of C stays put, the exponents are 3 and -13 which when I add that together gives me a negative 10. So at this step, I have negative 42 C raise the negative 10th power. Our directions specifically say we do not want to end up with a negative exponent. We want positive ex exponents. Only I recall that to make an exponent positive, I move it to the other half of my fraction. Right now. This doesn't look like a fraction, which means it's all in the numerator. So I'm going to create a fraction. I'm making a fraction bar and the base of C is gonna be in the denominator. And the exponent on C will be 10, a positive 10 because it went from the numerator to the denominator, which means it goes from a negative exponent to a positive exponent -42 stays in the numerator of my fraction. It didn't say we couldn't have negative numbers. It just said we wanted to have positive exponents. So we don't need to do anything with negative 42. That's OK. How it is also the exponent of negative 10 was only on the C base. It was not on the 42. So -42 over C raised to the 10th power is my answer. However, all of our answer choices are shown as division, not as fractions. So I'm gonna rewrite this as division. It would be negative 42 divided by C raised to the 10th power. And that's answer choice. C have a nice day.

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In Exercises 85–116, simplify each exponential expression.(2a⁵)(-3a⁻⁷)

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