Solve: 20¹⁰ × 4¹⁰ × 2¹⁰ - Multiplication of Powers Problem

Question

Insert the corresponding expression:

2010×410×210= 20^{10}\times4^{10}\times2^{10}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 When we are presented with a multiplication operation where all the factors have the same exponent (N)
00:06 All of the factors can be written to the power (N)
00:11 We will apply this formula to our exercise
00:19 This is the solution

Step-by-Step Solution

To solve the expression 2010×410×210 20^{10} \times 4^{10} \times 2^{10} , we can apply the Power of a Product rule for exponents. According to this rule, for any numbers a a , b b , and c c raised to the power of n n , we have:

an×bn×cn=(a×b×c)n a^n \times b^n \times c^n = (a \times b \times c)^n

In this case, we have:

  • a=20 a = 20

  • b=4 b = 4

  • c=2 c = 2 ,

  • n=10 n = 10 .

Thus, we can write:

2010×410×210=(20×4×2)10 20^{10} \times 4^{10} \times 2^{10} = (20 \times 4 \times 2)^{10}

Answer

(20×4×2)10 \left(20\times4\times2\right)^{10}