Use properties of rational exponents to simplify each expression. Assume that all variables repr

step 1 Here we have x to the one -fourth times y to the negative two -fifths all raised to the one -thi

Use properties of rational exponents to simplify each...

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Key Concepts

Properties of Exponents

This concept involves the laws that govern the operations on exponents, such as multiplying powers, dividing powers, and raising a power to another power. These rules allow us to combine and simplify expressions where variables are raised to various exponents by determining how exponents interact when operations like multiplication and exponentiation are applied.

Rational Exponents

Rational exponents are exponents that are fractions. They provide a way to represent roots in exponential form. For example, an exponent of 1/n corresponds to taking the nth root of a number, and more generally, an exponent expressed as m/n can be interpreted as taking the nth root of a number and then raising it to the mth power.

Negative Exponents

Negative exponents indicate the reciprocal of a base raised to the corresponding positive exponent. When a variable is raised to a negative exponent, it can be rewritten as the inverse of that variable raised to the positive exponent, which simplifies the expression and is helpful in further reducing complex expressions involving exponents.

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