Calculate the Product: 9^9 × 8^9 × 2^9 Powers Multiplication

Question

Insert the corresponding expression:

99×89×29= 9^9\times8^9\times2^9=

Video Solution

Solution Steps

00:00 Simply
00:03 When we have a product where each factor has the same exponent (N)
00:07 We can write the exponent (N) over the entire product
00:16 We will use this formula in our exercise
00:21 And this is the solution to the question

Step-by-Step Solution

To solve the expression 99×89×29 9^9 \times 8^9 \times 2^9 , we will apply the "Power of a Product" rule in the exponent rules. This rule states that if you have a product of terms all raised to the same exponent, it can be rewritten as the product itself raised to that exponent. The formula is given by:

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

In our problem, we can identify the terms as:

  • a=9 a = 9

  • b=8 b = 8

  • c=2 c = 2

  • n=9 n = 9

Applying the formula, we can convert the product of powers into a single power:

99×89×29=(9×8×2)9 9^9 \times 8^9 \times 2^9 = (9 \times 8 \times 2)^9

Answer

(9×8×2)9 \left(9\times8\times2\right)^9