Solution Bank Rational Exponents & Radicals Target C
Answers to the Practice Problems are below in random order.
\(\begin{align}&(2x-1)(4x^2+2x+1)\ & \ \ \ &x^3+10x^2+32x+32\ & \ \ \ &5x\strut^{\frac{4}{5}}\\\\
&157\ & \ \ \ &-19x\strut^{\frac{4}{5}}\ & \ \ \ &-21x\strut^{\frac{21}{20}}\\\\
&4x\strut^{\frac{11}{20}}\ & \ \ \ &x^2+6x+12\ & \ \ \ &\text{Notation means composition, not multiply;} h(g(x))=3x+14\\\\
&(2x+5i)(2x-5i)\ & \ \ \ &x^3+10x^2+32x+32\ & \ \ \ &16\sqrt[4]{3}\\\\
&(3x^2+4)^2\ & \ \ \ &x+2\ & \ \ \ &x^2+14x+44\\\\
&2x^4y^6z \cdot \sqrt[3]{7y^2z}\ & \ \ \ &49\ & \ \ \ &\text{Order matters:} f(g(x)) \ne g(f(x))\\\\
&g(x)=9x\strut^{\frac{1}{3}}\ & \ \ \ &g(x)=\frac{2}{3}x\strut^{\frac{5}{2}}\ & \ \ \ &\text{D}\\\\
&9x\strut^{\frac{5}{2}} \ & \ \ \ &15\ & \ \ \ &3x\strut^{\frac{5}{2}}\\\\
&\ & \ \ \ \end{align}\)
Answers to the Practice Problems are below in random order.
\(\begin{align}&(2x-1)(4x^2+2x+1)\ & \ \ \ &x^3+10x^2+32x+32\ & \ \ \ &5x\strut^{\frac{4}{5}}\\\\
&157\ & \ \ \ &-19x\strut^{\frac{4}{5}}\ & \ \ \ &-21x\strut^{\frac{21}{20}}\\\\
&4x\strut^{\frac{11}{20}}\ & \ \ \ &x^2+6x+12\ & \ \ \ &\text{Notation means composition, not multiply;} h(g(x))=3x+14\\\\
&(2x+5i)(2x-5i)\ & \ \ \ &x^3+10x^2+32x+32\ & \ \ \ &16\sqrt[4]{3}\\\\
&(3x^2+4)^2\ & \ \ \ &x+2\ & \ \ \ &x^2+14x+44\\\\
&2x^4y^6z \cdot \sqrt[3]{7y^2z}\ & \ \ \ &49\ & \ \ \ &\text{Order matters:} f(g(x)) \ne g(f(x))\\\\
&g(x)=9x\strut^{\frac{1}{3}}\ & \ \ \ &g(x)=\frac{2}{3}x\strut^{\frac{5}{2}}\ & \ \ \ &\text{D}\\\\
&9x\strut^{\frac{5}{2}} \ & \ \ \ &15\ & \ \ \ &3x\strut^{\frac{5}{2}}\\\\
&\ & \ \ \ \end{align}\)