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Chapter 0: Problem 15

Evaluate each exponential expression. $$\left(2^{2}\right)^{3}$$

Short Answer

Expert verified
The value of the expression \((2^{2})^{3}\) is 64.

Step by step solution

01

Identify the exponential form

The expression can be identified in the form:\(b^{m^{n}}\), where \(b\) is the base, \(m\) is the exponent on the base and \(n\) is the power on the whole expression. Here, \(2^{2}\) is the base and \(3\) is the power on that base.
02

Apply the rule of 'power of power'

The law of exponents states that when raising a power to a power, you multiply the exponents. This rule is called the 'power of power' rule, which is \((b^{m})^n = b^{m*n}\). Applying this rule will simplify the expression. Here, it becomes \(2^{2*3}\).
03

Simplify the expression

Simplify the expression further by multiplying the exponents. \(2^{2*3} = 2^6\).
04

Calculate the final value

2 raised to the power of 6 equals 64. So, \(2^{6} = 64\).

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