Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. -4r^-2(r^4)^2

Key Concepts

Exponents and Negative Exponents

Exponents represent repeated multiplication of a base number. A negative exponent indicates the reciprocal of the base raised to the absolute value of the exponent. For example, r^-2 can be rewritten as 1/r^2. Understanding how to manipulate negative exponents is crucial for simplifying expressions correctly.

Power of a Power Rule

The power of a power rule states that when raising a power to another power, you multiply the exponents. For instance, (r^4)^2 simplifies to r^(4*2) or r^8. This rule is essential for simplifying expressions involving exponents, especially when multiple exponent rules are applied together.

Combining Like Terms

Combining like terms involves simplifying expressions by adding or subtracting terms that have the same variable raised to the same power. In the expression -4r^-2(r^4)^2, after applying the power of a power rule, you will combine the resulting terms to achieve a simplified form. This concept is fundamental in algebra for reducing expressions to their simplest form.