Simplify each expression. Assume all variables represent nonzero ...

Question

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3.

-4m²
( ——— )⁴
      tp²

Accepted Answer

Hello, everyone. We are given an expression and asked to simplify it. The variables in this expression are all non-zero real numbers. The expression is open square bracket, parentheses, negative two A cubed closed parentheses divided by BC cubed closed bracket. Raised to the fifth power. Our answer choices are a negative 32 A raised to the 15th power divided by B raised to the fifth power C raised to the 15th power B 32 A raised to the eighth power divided by B raised to the sixth power C raised to the eighth power C negative 32 A squared divided by B raised to the fourth power C squared D 32 A squared divided by B raised to the fourth power C squared. So I'm gonna rerate this as a fraction because I think that'll help me see what I need to do. So I'm still gonna keep my square bracket but I have a numerator. Now that is negative two A cubed divided by the denominator which is BC, the C is cubed, closing my bracket and raising that whole thing to the fifth power. So writing it this way, I see a little clearer what I'm trying to do. I have a quotient that is raised to a power. And I recall when I have a quotient raise to a power, I raise both the numerator and the denominator to that power. So I'm gonna rewrite this as negative two a cubed in parentheses, raised to the fifth power divided by, in parentheses. BC cubed raised to the fifth power. So now I have two instances of a product being raised to a power. And when I have a product raised to a power, I recall that each base within that product will be raised to that power. So each factor will be raised to the fifth power in this case. So for our numerator, they'll give me negative two raise to the fifth power multiplied by a cubed race to the fifth power divided by our denominator which will be B raise the fifth power multiplied by C cubed raise to the fifth power. So next, when I have a power raised to a power, I multiply my exponents. And if my base is a constant, I'm gonna use the actual math and find out what the value is. So negative two raised to the fifth power would be negative 32. And then a cubed raised to the fifth power, I multiply my exponents. So this would be a raised to the 15th power divided by be raised to the fifth power. We'll just say B raise the fifth power C cubed to raise the fifth power again. When we raise a power to a power, we multiply our exponents and keep the base. So it'll be C to the 15th power. So this is our answer. Negative 32. A raise the 15th power divided by B raise the fifth power. C raise the 15th power and this matches answer choice A have a nice day.

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Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. -4m² ( ——— )⁴ tp²