Simplify: 4^(2y) × 4^(-5) × 4^(-y) × 4^6 Using Laws of Exponents

Question

42y⋅4−5⋅4−y⋅46= 4^{2y}\cdot4^{-5}\cdot4^{-y}\cdot4^6=

Video Solution

Solution Steps

00:00 Simplify the expression
00:03 When multiplying powers with the same base, add the exponents
00:07 This formula is relevant for any number of bases
00:13 Let's use this formula in our exercise
00:17 Let's sum all the exponents
00:28 Let's group the factors
00:38 And this is the solution to the question

Step-by-Step Solution

We use the power property to multiply terms with identical bases:

am⋅an=am+n a^m\cdot a^n=a^{m+n} We apply the property for this problem:

42y⋅4−5⋅4−y⋅46=42y+(−5)+(−y)+6=42y−5−y+6 4^{2y}\cdot4^{-5}\cdot4^{-y}\cdot4^6= 4^{2y+(-5)+(-y)+6}=4^{2y-5-y+6} We simplify the expression we got in the last step:

42y−5−y+6=4y+1 4^{2y-5-y+6} =4^{y+1} When we add similar terms in the exponent.

Therefore, the correct answer is option c.

Answer

4y+1 4^{y+1}

More Questions

Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Multiplying Exponents with the Same Base

Question Types

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