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Sagot :
[tex]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}}[/tex]
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)
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