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

Question

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

(-6x²)³

Accepted Answer

Welcome back. I am so glad you're here. We're told for the following expression. Simplify note that the variable K is a nonzero real number. Our expression is negative three KQ all raised to the fourth power. Our answer choices are answer choice. A negative 81 K raised to the 12th power. Answer choice B negative 81 K raised to the seventh power answer choice C 81 K raised to the 12th power and answer choice. D 81 K raised to the seventh power. All right. So we have this term being raised to a power. There are two parts to the term we've got this negative three and the K cubed, both of those are being raised to the fourth power. So if we look first at the negative three, raised to the fourth power, that negative three is being multiplied by itself four times. So because that's an even number of times, it's being multiplied by itself, it's going to end up being a positive 81. Now, how about this K cubed raised to the fourth power. We recall from previous lessons, the power to a power rule. We're raising this third power up to the fourth power. And when we do that, we are going to multiply the exponents. So three multiplied by four is 12. We've got A K raised to the 12th power. So the whole thing simplified is 81 K to the 12th. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. (-6x²)³

Key Concepts

Exponentiation

Negative Exponents

Polynomial Expansion

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