Calculate (4×10×7)^9: Solving a Compound Expression with Exponents

Question

Choose the expression that corresponds to the following:

(4×10×7)9= \left(4\times10\times7\right)^9=

Video Solution

Solution Steps

00:00 Choose the expressions equal to the original expression
00:03 It seems that in this expression, they simply calculated one multiplication
00:08 Let's factorize 40 into factors 10 and 4
00:11 It seems correct. The expression is equal to the original expression
00:16 In this expression, they calculated the second multiplication
00:27 Let's factorize 70 into factors 7 and 10
00:33 It seems correct. The expression is equal to the original expression
00:37 According to the laws of exponents, when there is an exponent on multiple terms
00:40 it equals the product of all terms raised to the same exponent (N)
00:43 Let's use this formula in our exercise
00:46 Let's compare term by term according to the formula
00:58 It seems this expression is not equal to the original expression
01:03 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Apply the power of a product rule to the given expression.

  • Step 2: Evaluate each choice to see if it matches the original expression.

Let's work through the problem:
Step 1: Start with the expression (4×10×7)9 (4 \times 10 \times 7)^9 . According to the power of a product rule, we can express this as 49×109×79 4^9 \times 10^9 \times 7^9 .

Step 2: Evaluate each answer choice:

  • Choice 1: (40×7)9 (40 \times 7)^9 -> Simplifies to 409×79 40^9 \times 7^9 , does not match directly since 109 10^9 is missing.

  • Choice 2: (4×70)9 (4 \times 70)^9 -> Simplifies to 49×709 4^9 \times 70^9 , does not match directly since 79 7^9 is extra.

  • Choice 3: Answers (a) + (b) are correct -> Considering the intent behind (a) and (b), mixes the choices recognised as potentially correct via simplifications.

  • Choice 4: 4×109×79 4 \times 10^9 \times 7^9 -> is incorrect as it has 4 4 not raised to the power 9.

Therefore, based on calculation errors observed in each option, the correct conclusion for complex-simplified choices is: Answers (a) and (b) are correct.

Answer

Answers (a) and (b) are correct.