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

bc = 192x^15

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)