Simplify each expression. Write all answers with positive...

Simplify each expression. Write all answers with positive exponents. Assume that all variables represent positive real numbers. See Example 5 .
$$
\left(\frac{m^{-2 / 3}}{a^{-3 / 4}}\right)^{4}\left(m^{-3 / 8} a^{1 / 4}\right)^{-2}
$$

Key Concepts

Exponent Laws

Exponent laws are a set of rules used to manipulate expressions involving powers. They include operations such as multiplying and dividing exponential expressions with the same base and raising a power to another power. These rules are fundamental for simplifying algebraic expressions involving exponents.

Negative Exponent Rule

The negative exponent rule states that any expression with a negative exponent can be rewritten as the reciprocal of the expression with a positive exponent. This is crucial in rewriting and simplifying expressions to avoid negative exponents, ensuring that all exponents are positive.

Power of a Power and Power of a Product/Quotient Rules

These rules allow one to simplify expressions where an exponent is raised to another exponent (power of a power) or where an exponent is applied to a product or quotient. By applying the exponent to each factor in the product or numerator and denominator in the quotient, the expression can be simplified systematically while maintaining the correct order of operations.

Rational Exponents

Rational exponents represent both exponentiation and root extraction in one notation. They follow the same exponent laws as integer exponents, allowing for the simplification and conversion of expressions with fractional (rational) exponents into more conventional forms with positive exponents.

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