Solve the examples below. The answer should contain only positive indicators without fractional indicators in the denominator. Leave Rational (Not Radical) Answers: 1) (343b^{3})^frac{4}{3} 2) (216x^{6})^{-frac{5}{3}} 3) 3a^{-2}b^{frac{5}{4}}times 2a^{-frac{7}{4}}b^{frac{4}{3}}

Question

Solve the examples below. The answer should contain only positive indicators without fractional indicators in the denominator. Leave Rational (Not Radical) Answers:

1) (343 b^{3})^{\frac{4}{3}}

2) (216 x^{6})^{- \frac{5}{3}}

3) 3 a^{- 2} b^{\frac{5}{4}} \times 2 a^{- \frac{7}{4}} b^{\frac{4}{3}}

Answer 1

Step 1

(343 b^{3})^{\frac{4}{3}} = ((7 b)^{3})^{\frac{4}{3}}

= (7 b)^{3 \times \frac{4}{3}}

= (7 b)^{4}

= 7^{4} b^{4}

= 2401 b^{4}

Step 2

(216 x^{6})^{- \frac{5}{3}} = (6^{3} x^{6})^{- \frac{5}{3}}

= (6^{3})^{- \frac{5}{3}} \times (x^{6})^{- \frac{5}{3}}

= 6^{- 3 \times - \frac{5}{3}} \times x^{6 \times - \frac{5}{3}}

= 6^{- 5} x^{- 10}

= \frac{1}{6^{5} x^{10}}

= \frac{1}{(6 x^{2})^{5}}

Step 3

3 a^{- 2} b^{\frac{5}{4}} \times 2 a^{- \frac{7}{4}} b^{\frac{4}{3}} = 6 a^{- 2 - \frac{7}{4}} b^{\frac{5}{4} + \frac{4}{3}}

= 6 a^{- \frac{15}{4}} b^{\frac{31}{12}}

= \frac{6 b^{\frac{31}{12}}}{a^{\frac{15}{4}}}

= \frac{6 b^{\frac{31}{12}} a^{\frac{1}{4}}}{a^{\frac{15}{4} + \frac{1}{4}}}

= \frac{6 b^{\frac{31}{12}} a^{\frac{1}{4}}}{a^{\frac{16}{4}}}

= \frac{6 b^{\frac{31}{12}} a^{\frac{1}{4}}}{a^{4}}

Solve the examples below. The answer should contain only positive indicators without fractional indicators in the denominator. Leave Rational (Not Radical) Answers: 1) (343b^{3})^frac{4}{3} 2) (216x^{6})^{-frac{5}{3}} 3) 3a^{-2}b^{frac{5}{4}}times 2a^{-frac{7}{4}}b^{frac{4}{3}}

Expert Answer

Not exactly what you’re looking for?

Relevant Questions