Question

27 (6x)^3 =
a 6x^3 b 9x^3 c 18x^3 d 27x^3 e 216x^3
28 (16x^{-6}y^2)^{-1} =
a \frac{x^3}{4y} b \frac{x^6}{16y^2} c \frac{4x^3}{y} d -\frac{4x^3}{y}
29 write in simplest form, using positive integral exponents: (\frac{ay^2}{b^4})^3(\frac{b}{y^3})^5
a \frac{a^3}{b^7y^9} b \frac{a^3b^2}{y^3} c \frac{a^3}{b^7y^3} d \frac{a^3}{b^7y^4}

Explanation:

Step1: Solve 27

Use power - of - a - product rule $(ab)^n=a^n\times b^n$. Here $(6x)^{3}=6^{3}\times x^{3}=216x^{3}$.

Step2: Solve 28

Use negative - exponent rule $(a^{m}b^{n})^{-p}=\frac{1}{a^{mp}b^{np}}$. So $(16x^{-6}y^{2})^{-1}=\frac{1}{16x^{-6}y^{2}}=\frac{x^{6}}{16y^{2}}$.

Step3: Solve 29

First, use power - of - a - quotient rule $(\frac{m}{n})^p=\frac{m^p}{n^p}$.
$(\frac{ay^{2}}{b^{4}})^{3}(\frac{b}{y^{3}})^{5}=\frac{a^{3}y^{6}}{b^{12}}\times\frac{b^{5}}{y^{15}}$.
Then use product rule of exponents $\frac{a^{m}}{a^{n}}=a^{m - n}$.
$\frac{a^{3}y^{6}}{b^{12}}\times\frac{b^{5}}{y^{15}}=\frac{a^{3}y^{6 - 15}}{b^{12-5}}=\frac{a^{3}}{b^{7}y^{9}}$.

Answer:

1. E. $216x^{3}$
2. B. $\frac{x^{6}}{16y^{2}}$
3. C. $\frac{a^{3}}{b^{7}y^{3}}$