Simplify ((4x)^(3y))^2: Working with Double Exponents

Question

((4x)3y)2= ((4x)^{3y})^2=

Video Solution

Solution Steps

00:00 Simplify the expression
00:03 When there is a power of a power, the common power is the product of the powers
00:07 We will use this formula in our exercise
00:13 We'll multiply by each of the powers
00:19 We'll calculate the product of the power
00:28 When there's a power on a product of multiple terms, they all rise to that power
00:33 We'll use this formula in our exercise to factorize
00:39 And this is the solution to the question

Step-by-Step Solution

We'll use the power rule for powers:

(am)n=am⋅n (a^m)^n=a^{m\cdot n} We'll apply this rule to the expression in the problem:

((4x)3y)2=(4x)3y⋅2=(4x)6y ((4x)^{3y})^2= (4x)^{3y\cdot2}=(4x)^{6y} When in the first stage we applied the mentioned power rule and eliminated the outer parentheses, in the next stage we simplified the resulting expression,

Next, we'll recall the power rule for powers that applies to parentheses containing a product of terms:

(a⋅b)n=an⋅bn (a\cdot b)^n=a^n\cdot b^n We'll apply this rule to the expression we got in the last stage:

(4x)6y=46y⋅x6y (4x)^{6y} =4^{6y}\cdot x^{6y} When we applied the power to the parentheses to each term of the product inside the parentheses.

Therefore, the correct answer is answer D.

Answer

46y⋅x6y 4^{6y}\cdot x^{6y}

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 Power of a Power: Using multiple rules Applying Combined Exponents Rules: Two Variables Applying Combined Exponents Rules: Variables in the exponent of the power Applying Combined Exponents Rules: Monomial Applying Combined Exponents Rules: Using multiple rules