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

Question

(9×2×5)3= (9\times2\times5)^3=

Video Solution

Solution Steps

00:00 Simplify the expression
00:02 When there is a power on a product of terms, all terms are raised to that power

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.

Answer

93×23×53 9^3\times2^3\times5^3

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Related Subjects

Exponents and Exponent rules Rules of Exponentiation Combining Powers and Roots Properties of Exponents Exponent of a Multiplication

Question Types

Applying Combined Exponents Rules: Trinomial Applying Combined Exponents Rules: Applying the formula Applying Combined Exponents Rules: A power law Power of a Product: Applying the formula