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Simplify (2x^3)(5x^4)

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Answer
10x7\boxed{10x^7}

Checking the result by expanding the terms gives (2⋅x⋅x⋅x)(5⋅x⋅x⋅x⋅x)=10x7(2 \cdot x \cdot x \cdot x)(5 \cdot x \cdot x \cdot x \cdot x) = 10x^7.

Problem: Simplify the expression (2x3)(5x4)(2x^3)(5x^4).

Steps

  1. Rearrange using the commutative and associative properties
    (2⋅5)(x3⋅x4)(2 \cdot 5)(x^3 \cdot x^4)
  2. Multiply the coefficients and apply the product rule for exponents (xa⋅xb=xa+bx^a \cdot x^b = x^{a+b})
    10x3+410x^{3+4}
  3. Add the exponents
    10x710x^7

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