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

Question

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

Video Solution

Solution Steps

00:00 Simplify the expression
00:03 When there is a power of a power, the combined exponent is the product of the exponents
00:07 Let's use this formula in our exercise
00:12 Multiply by each of the powers
00:21 Solve one multiplication at a time
00:35 And this is the solution to the question

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}

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