Final answer:
To find the cube root of the expression (5x³)(4x)³, each term is raised to the power of three and then multiplied together, which results in 320x¶. Therefore the correct answer is B) 320x¶.
Step-by-step explanation:
The student is asking for the cube root of the expression (5x³)(4x)³. To find the cube root of this expression, we follow the rules for exponentiation and multiplication of powers.
Firstly, we raise each part of the expression to the respective power. For the first part, 5x³, it is already in cubic form, so we take it as it is. For the second part, (4x)³, we need to raise both the coefficient (4) and the variable (x) to the power of 3. Here's the algebraic breakdown:
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- (5x³) means 5 × (x × x × x)
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- (4x)³ means (4³) × (x³) which is 64x³
Now, we multiply (5x³) by (64x³) which results in (5 × 64) × (x³ × x³). Multiplying the coefficients (5 × 64) gives us 320, and for the variables, since we are multiplying like terms, we add the exponents (3+3) which results in x⁶ or x¶.
Therefore, the result is 320x¶, and the correct answer to the given question is option B) 320x¶.