Solve Triple Nested Exponents: ((y^6)^8)^9 Simplification Challenge

Question

((y6)8)9= ((y^6)^8)^9=

Video Solution

Solution Steps

00:00 Solve
00:02 When there's a power of a power, the combined exponent is the product of the exponents
00:05 We'll solve one multiplication at a time
00:08 And this is the solution to the question

Step-by-Step Solution

We use the power rule of distributing exponents.

(am)n=am⋅n (a^m)^n=a^{m\cdot n} We apply it in the problem:

((y6)8)9=(y6⋅8)9=y6⋅8⋅9=y432 \big((y^6)^8\big)^9=(y^{6\cdot8})^9=y^{6\cdot8\cdot9}=y^{432} When we use the aforementioned rule twice, the first time for the inner parentheses in the first stage and the second time for the remaining parentheses in the second stage, in the last stage we calculate the result of the multiplication in the power exponent.

Therefore, the correct answer is option b.

Answer

y432 y^{432}

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: Variable in the base of the power Applying Combined Exponents Rules: Single Variable Applying Combined Exponents Rules: Variable in the base of the power Applying Combined Exponents Rules: A power law