Solve Nested Exponents: ((14^(3x))^(2y))^(5a) Simplification

Question

((143x)2y)5a= ((14^{3x})^{2y})^{5a}=

Video Solution

Solution Steps

00:10 Let's simplify this expression together.
00:14 When you have a power raised to another power, multiply the exponents together.
00:19 Now, let's use this rule in our example.
00:23 Multiply each of the exponents carefully.
00:31 Take it step by step, solving one multiplication at a time.
00:45 Great job! That's your solution.

Step-by-Step Solution

Using the power rule for an exponent raised to another exponent:

(am)n=am⋅n (a^m)^n=a^{m\cdot n} We apply the rule to the given problem:

((143x)2y)5a=(143x)2y⋅5a=143x⋅2y⋅5a=1430xya ((14^{3x})^{2y})^{5a}=(14^{3x})^{2y\cdot5a}=14^{3x\cdot2y\cdot5a}=14^{30xya} In the first step we applied the aforementioned power rule and removed the outer parentheses. In the next step we again applied the power rule and removed the remaining parentheses.

In the final step we simplified the resulting expression,

Therefore, through the rule of substitution (which is applied to the exponent of the power in the obtained expression) it can be concluded that the correct answer is answer D.

Answer

1430axy 14^{30axy}

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Related Subjects

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

Question Types

Applying Combined Exponents Rules: Variables in the exponent of the power Power of a Power: Variables in the exponent of the power