The Power Of A Power Property: Simplifying Exponential Expressions With Ease

power of a power property

(a^x)^y = a^xy

The power of a power property is an exponent rule that states that when you raise a power to another power, you can simplify the expression by multiplying the exponents. Specifically, we have:

(a^n)^m = a^(n*m)

That is, when we have a base a raised to an exponent n, and the entire expression is raised to another exponent m, we can multiply the exponents n and m to rewrite the expression as a raised to the product of n and m.

For example, consider the expression (3^2)^4. By applying the power of a power property, we can simplify this as follows:

(3^2)^4 = 3^(2*4) = 3^8

Thus, (3^2)^4 is equivalent to 3 raised to the 8th power.

It’s important to note that the power of a power property applies only when the base is the same in both exponents. If the bases are different, we cannot simplify the expression using this rule.

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