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

(9×2×5)3= (9\times2\times5)^3=

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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

Test your knowledge with interactive questions

Choose the expression(s) that corresponds to the following:

\( \left(5\times6\right)^9= \)

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Exponents Rules questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

More Questions

Click on any question to see the complete solution with step-by-step explanations

Applying Combined Exponents Rules

Simplify the Expression: m^(-n) × n^(-m) × 1/m
Click to solve
Solve (a×b×8)²: Square of a Triple Product Expression
Click to solve

Exponents Rules

Simplify the Expression: x³·x⁴·(2/x³)·x⁻⁸ Using Laws of Exponents
Click to solve
Simplify the Expression: y³ · y⁻⁴ · (-y)³ ÷ y⁻³
Click to solve

Power of a Product

Calculate (x×4×3)³: Cube of a Three-Term Product
Click to solve
Evaluate (a·5·6·y)^5: Simplifying a Fifth Power Expression
Click to solve