Evaluate (5×6)^9: Solving a Multiple-Step Exponent Problem

Question

Insert the corresponding expression:

(5×6)9= \left(5\times6\right)^9=

Video Solution

Solution Steps

00:00 Simply
00:03 To open parentheses with an exponent on a product
00:06 Raise each factor to the power
00:11 We'll use this formula in our exercise
00:18 And this is the solution to the question

Step-by-Step Solution

To solve the expression (5×6)9 \left(5\times6\right)^9 , we apply the rule for the power of a product. This rule states that when you raise a product to a power, it is equivalent to raising each factor in the product to the same power. Mathematically, this is expressed as:

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

In this specific problem, the factors are 5 5 and 6 6 and the exponent is 9 9 . Applying the power of a product rule, we get:

  • (5×6)9=59×69 \left(5\times6\right)^9 = 5^9 \times 6^9

Therefore, the correct expression that corresponds to (5×6)9 \left(5\times6\right)^9 is 59×69 5^9\times6^9 .

Answer

59×69 5^9\times6^9