(3^2)^2 Simplified

Suzhoumeite

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Jul 03, 2024

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Simplifying (3^2)^2

In this article, we will simplify the expression (3^2)^2 and explore the rules of exponentiation that make it possible.

Understanding Exponentiation

Before we dive into simplifying the expression, let's quickly review the rules of exponentiation.

• Exponent: The small number that tells us how many times to multiply a number by itself. For example, in 2^3, the 3 is the exponent.
• Base: The number being multiplied by itself. For example, in 2^3, the 2 is the base.
• Power: The result of raising the base to the exponent. For example, 2^3 = 2 × 2 × 2 = 8.

Simplifying (3^2)^2

Now, let's break down the expression (3^2)^2:

• 3^2 means "3 to the power of 2", which equals 3 × 3 = 9.
• So, (3^2) equals 9.
• Now, we need to raise 9 to the power of 2, which means multiplying 9 by itself: 9 × 9 = 81.

Therefore, (3^2)^2 simplifies to 81.

Why This Works

This simplification is possible because of the power of a power rule, which states that when you raise a number to a power, and then raise the result to another power, you can multiply the exponents.

In this case, (3^2)^2 = 3^(2×2) = 3^4 = 81.

Conclusion

In conclusion, we have successfully simplified the expression (3^2)^2 to its simplest form, 81, using the rules of exponentiation and the power of a power rule.