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

Question

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

r⁸
( —— )³
     s²

Accepted Answer

Hello, everyone. We are asked to simplify the following expression. It is noted that the variables in the expression are nonzero real numbers. The expression we are given is in parentheses. U raised to the sixth power divided by V cubed closed parentheses. Raise to the fourth power. Our answer choices are a U raise to the 24th power V raised to the 12th power bu raised to the 10th power divided by V. Raised to the seventh power cu raised to the 24th power divided by V. Raised to the 12th power du raised to the 10th power V to begin with. I'm going to rewrite our expression as a fraction. So I have U raise the sixth power divided by V cubed in parentheses, raised to the fourth power. I recall that when I have a fraction raised to a power or a quotient raised to a power, I am going to raise both the numerator and the denominator to that power. So we'll have you to the sixth power. Raise the fourth power divided by V to the third power raised to the fourth power from there. Recall that when we have a power raised to a power. That rule says we multiply our exponents. So for you, in the numerator, we will do six multiplied by four, which is 24. So we have you raise the 24th power. And in our denominator, we have V raised to the third power raised to the fourth power which when I multiply three and four, I get V raised to the 12th power. So this fraction is our answer. You raise the 24th power divided by V raised to the 12th power, which is answer choice. C have a nice day.

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 2 and 3. r⁸ ( —— )³ s²

Key Concepts

Exponent Rules

Simplifying Fractions

Nonzero Real Numbers

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