Solve: (2²)³ + (3³)⁴ + (9²)⁶ - Nested Exponents Challenge

Question

(22)3+(33)4+(92)6= (2^2)^3+(3^3)^4+(9^2)^6=

Video Solution

Solution Steps

00:00 Solve the following problem
00:03 When there is a power over a power, the shared power is the product of the powers
00:07 This is the solution

Step-by-Step Solution

We use the formula:

(am)n=am×n (a^m)^n=a^{m\times n}

(22)3+(33)4+(92)6=22×3+33×4+92×6=26+312+912 (2^2)^3+(3^3)^4+(9^2)^6=2^{2\times3}+3^{3\times4}+9^{2\times6}=2^6+3^{12}+9^{12}

Answer

26+312+912 2^6+3^{12}+9^{12}

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Power of a Power

Question Types

Power of a Power: Number of terms Power of a Power: Applying the formula Applying Combined Exponents Rules: Number of terms Applying Combined Exponents Rules: Trinomial Applying Combined Exponents Rules: Applying the formula Applying Combined Exponents Rules: A power law