In Exercises 85–116, simplify each exponential expression.

20x³/...

Question

In Exercises 85–116, simplify each exponential expression.

20x³/-5x⁴

Accepted Answer

Hello, everyone. We've been asked to simplify the following expression and write the answer with positive exponents. The expression we're given is open parentheses. 49 K raised to the seventh power closed parentheses divided by open parentheses. Negative seven K raised to the 11th power closed parentheses. Our answer choices are a negative seven K raised the 44th power B -7 K raised to the 4th power C - divided by K to the 18th power D -7 divided by K to the 4th power. I'm going to rewrite my original expression as a fraction so I can write it as 49K raise to the 7th power Over -7 K raised the 11th power. I recall that even though I have variables with exponents, the constant or the coefficients in this case will still hold the same rules of division that I've known my entire life. So 49 divided by negative seven is negative seven that is in our numerator at this point. And now that we've dealt with it, we can move on to dealing with the variables. Recall that variables with like bases that have exponents, keep their base the same. And in division, we subtract our exponents. So this would be K raised to the 7 - power if I want to simplify that this is the same thing as saying negative seven K to the negative fourth power. And I recall that I don't want any negative exponents, the directions say we want positive exponents. So the negative exponent is on the base of K. So the base K is going to move to the denominator of my fraction. The exponent is gonna go from a negative four to a positive four. But the value -7 is gonna stay in the numerator because the exponent was only on the K, not on the -7. This is my solution negative seven over K to the fourth power. How this is written in your answer choices is as a division problem. So that would be the same as saying negative seven divided by K raised to the fourth power. And that is answer choice D have a nice day.

In Exercises 85–116, simplify each exponential expression. 20x³/-5x⁴

Key Concepts

Exponential Expressions

Simplifying Rational Expressions

Factoring Polynomials

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