Rules of Exponents: Simplifying Terms with Different Bases

How do we simplify terms with different bases using the rules of exponents?

Given: (7x^(-3))(-2x^(2)y^(5))(-y^(-4)z^(6))

Answer:

The product of the terms (7x^(-3))(-2x^(2)y^(5))(-y^(-4)z^(6)) is simplified to 14x^(-1)y^(1)z^(6).

The problem asks us to simplify the given expression (7x^(-3))(-2x^(2)y^(5))(-y^(-4)z^(6)). To do this, we need to remember a few basic principles of exponents: when you multiply terms with the same base, you add the exponents; and when you have a term raised to a negative exponent, it is equivalent to the reciprocal of the term raised to the positive exponent. Thus, the simplified form of the given expression is 14x^(-1)y^(1)z^(6), which corresponds to the first option. In other words, the product of the terms simplifies to 14 times x raised to the power of -1, y to the power of 1, and z to the power of 6.