Question

select the correct answer.
which expression is equivalent to the given expression?
$(7y^{6})(2y^{-4})^{2}$
$\frac{14}{y^{18}}$
$14$
$\frac{28}{y^{2}}$
$28y^{14}$

Explanation:

Step1: Expand the squared term

Use exponent rule $(a^m)^n=a^{m \times n}$:
$(2y^{-4})^2 = 2^2 \times y^{-4 \times 2} = 4y^{-8}$

Step2: Multiply with the first term

Multiply coefficients and add exponents (rule $a^m \times a^n=a^{m+n}$):
$7y^6 \times 4y^{-8} = (7 \times 4) \times y^{6 + (-8)} = 28y^{-2}$

Step3: Rewrite negative exponent

Use rule $a^{-m}=\frac{1}{a^m}$:
$28y^{-2} = \frac{28}{y^2}$

Answer:

$\frac{28}{y^2}$ (corresponding to the third option)