Question

simplify ((7y^{\frac{4}{5}})(16y)^{\frac{1}{4}}).

select one:
a. (14y^{\frac{21}{20}})
b. (14y^{\frac{4}{20}})
c. (112y^{\frac{21}{20}})
d. (14y^{\frac{5}{9}})

Explanation:

Step1: Separate constants and variables

$(7 \times 16) \times (y^{\frac{4}{5}} \times y^{\frac{1}{4}})$

Step2: Calculate constant product

$7 \times 16 = 112$

Step3: Combine variable terms

Use exponent rule $a^m \times a^n = a^{m+n}$:
$y^{\frac{4}{5} + \frac{1}{4}} = y^{\frac{16}{20} + \frac{5}{20}} = y^{\frac{21}{20}}$

Step4: Combine results

$112 \times y^{\frac{21}{20}}$

Answer:

C. $112y^{\frac{21}{20}}$