Calculate (9×2×5)³: Cube of a Three-Number Product

(9×2×5)3= (9\times2\times5)^3=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's begin!
00:07 We'll use the power rule for multiplication.
00:11 Any number multiplied and then raised to the power of N...
00:15 Means each number is separately raised to the power N.
00:19 We'll use this idea in our exercise.
00:22 Let's expand the brackets and raise each number to its power.
00:27 And there you have it, that's the solution!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

(9×2×5)3= (9\times2\times5)^3=

2

Step-by-step solution

We use the law of exponents for a power that is applied to parentheses in which terms are multiplied:

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

We apply the rule to the problem:

(9⋅2⋅5)3=93⋅23⋅53 (9\cdot2\cdot5)^3=9^3\cdot2^3\cdot5^3

When we apply the power within parentheses to the product of the terms we do so separately and maintain the multiplication,

Therefore, the correct answer is option B.

3

Final Answer

93×23×53 9^3\times2^3\times5^3

Practice Quiz

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

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