Simplify (2×3×7×9) Raised to Power (ab+3): Complete Expression Solution

Simplify:

(2⋅3⋅7⋅9)ab+3 (2\cdot3\cdot7\cdot9)^{ab+3}

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Simplify the following expression
00:03 When there is a power on a product of terms, all terms are raised to that power
00:13 We will use this formula in our exercise
00:17 Raise each factor to the power
00:32 This is the solution

Step-by-step written solution

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1

Understand the problem

Simplify:

(2⋅3⋅7⋅9)ab+3 (2\cdot3\cdot7\cdot9)^{ab+3}

2

Step-by-step solution

We begin by using the distributive law of exponents.

(x⋅y)n=xn⋅yn (x\cdot y)^n=x^n\cdot y^n

We apply this property to the given problem :

(2⋅3⋅7⋅9)ab+3=2ab+33ab+37ab+39ab+3 (2\cdot3\cdot7\cdot9)^{ab+3} =2^{ab+3}3^{ab+3}7^{ab+3}9^{ab+3}

When we apply the power of parentheses to each of the terms of the product inside the parentheses separately and maintain the multiplication.

Therefore, the correct answer is option a.

3

Final Answer

2ab+33ab+37ab+39ab+3 2^{ab+3}3^{ab+3}7^{ab+3}9^{ab+3}

Practice Quiz

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\( 112^0=\text{?} \)

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