Question

If a=3x^3, b=4x^4, and c=ab^2, then what is the value of bc?

Answer 1

$a=3x^3\hspace{5em}b=4x^4 \\\\[-0.35em] ~\dotfill\\\\ c=ab^2\implies c=(\underset{a}{3x^3})(\underset{b}{4x^4})^2\implies c=(3x^3)(4^2x^{4\cdot 2}) \\\\\\ c=3x^3\cdot 16x^8\implies c=(3\cdot 16)x^{3+8}\implies c=48x^{11} \\\\[-0.35em] ~\dotfill\\\\ \boxed{bc}\implies (\underset{b}{4x^4})(\underset{c}{48x^{11}})\implies (4\cdot 48)x^{4+11}\implies \boxed{192x^{15}}$

Answer 2

Answer:

  bc = 192x^15

Step-by-step explanation:

Perform substitution as required, then simplify.

Evaluation

  bc = b(ab^2) = ab^3 = (3x^3)(4x^4)^3 = (3·4^3)(x^3)(x^(4·3))

  = 192x^(3+12)

  bc = 192x^15

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Additional comment

The relevant rules of exponents are ...

  (ab)^c = (a^c)(b^c)

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)