In Exercises 85–116, simplify each exponential expression.

30x²y...

Question

In Exercises 85–116, simplify each exponential expression.

30x²y⁵/-6x⁸y⁻³

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. 52 C raised the 13th power D raised the fourth power closed parentheses divided by open parentheses. Negative 13 C raised the seventh power D raised the negative eighth power closed parentheses. Our answer choices are a negative four C raised. The sixth power D raised the 12th power B open parentheses. Negative four C raise the sixth power closed parentheses divided by D raise the 12th power C open parentheses, negative four C raised to the 20th. Power closed parentheses divided by D raised to the fourth power D -4 C raised the 20th power d raised the 4th power. The first thing I'm gonna do when I rewrite this is I'm gonna rewrite this expression as a fraction. So my numerator is gonna be my first set of parentheses. My denominator is my second set of parentheses. I find that this helps me see what I'm working with a little clearer. So 52 C raise the 13th power D raise the fourth power fraction bar negative 13 C raised the seventh power. D raised the negative eighth power. So now that I have this written down, I'm gonna start simplifying it. I'm gonna combine my like bases. So I'm gonna begin with 52 divided by -13, 52, divided by -14 is -4. This is the numerator of our new fraction, but I'm not gonna rewrite it as a fraction just yet until I'm done. Simplifying. Next, I'm gonna combine the bases of the variable C. I recall that when I divide like bases, I subtract their exponents. So this would be the same as saying C raised the 13 -7 power. And I'm gonna simplify that in my next step. Then I'm gonna do D so I have D to the fourth divided by D to the negative eighth. So this is like D raised to the four minus negative eight power because again, when I divide like bases, I subtract their exponents. So simplifying this, I have negative four C and then the exponent on C is gonna come from 13 -7 which is six. Then the base of D and the X one is from four minus negative eight which double negatives are like adding. So that's 12. And this is our simplification. It is negative four C raise the sixth power D raised to the 12th power. And that is answer choice. A have a nice day.

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In Exercises 85–116, simplify each exponential expression. 30x²y⁵/-6x⁸y⁻³