(3^7)^2 As A Single Power

Jasonbradley

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Jun 16, 2024

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Simplifying (3^7)^2 as a single power

In mathematics, we often encounter expressions involving exponents raised to another exponent, like (3^7)^2. This situation requires understanding a key property of exponents: the power of a power rule.

The Power of a Power Rule

This rule states that when raising a power to another power, we multiply the exponents. Mathematically:

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

Applying the Rule to (3^7)^2

Following the power of a power rule, we can simplify (3^7)^2 as follows:

• Identify the base and exponents:

  • The base is 3.
  • The first exponent is 7.
  • The second exponent is 2.

• Multiply the exponents: 7 * 2 = 14

• Rewrite the expression: (3^7)^2 = 3^(7*2) = 3^14

Therefore, (3^7)^2 simplified as a single power is 3^14.