Which property states to multiply the exponents when raising a power to another power?

The correct choice, which states to multiply the exponents when raising a power to another power, is known as the Power of a Power Property. This property mathematically expresses that when you take an exponent, say (a^m), and raise it to another exponent (n), you multiply the exponents:

[

(a^m)^n = a^{m \cdot n}

]

This means if you have (2^3) raised to the 4th power, it would be calculated as follows:

[

(2^3)^4 = 2^{3 \cdot 4} = 2^{12}

]

Understanding this property is crucial because it simplifies calculations involving exponents and allows for more complex algebraic manipulations.

The other choices refer to different exponent laws. The Product of Powers property involves adding exponents when multiplying two powers with the same base, while the Quotient of Powers property details how to subtract exponents when dividing powers with the same base. Lastly, the Power of a Quotient covers the rule for raising a fraction to a power by applying the exponent to both the numerator and the denominator, again indicating differences in how exponents function in various operations. Each of