Question

Please help, need answer fast!

Answer 1

Answer:

The correct answer is C

$\frac{12ac^{14}}{b^3}$

Step-by-step explanation:

We want to simplify

$\frac{(a^2b^4c)^{2}(6a^3b)(2c^5)^3}{4a^6b^{12}c^3}$.

Recall  this property of exponents,

$(a^m)^n=a^{mn}$

When we apply this property our expression becomes,

$=\frac{(a^4b^8c^2)(6a^3b)(2^3c^15)}{4a^6b^{12}c^3}$.

We rearrange to get

$=\frac{6\times8\times a^4\times a^3 \times b^8\times b\times c^2\times c^{15}}{4a^6b^{12}c^3}$.

We now apply another property of exponents to simplify the numerator.

According to this property,

$a^m\times a^n=a^{m+n}$

When we apply this property, the expression will now be,

$=\frac{6\times8\times a^{4+3} \times b^{8+1} c^{2+15}}{4a^6b^{12}c^3}$

This simplifies to,

$=\frac{48\times a^{7} \times b^{9} c^{17}}{4a^6b^{12}c^3}$

We again apply this property of exponents,

$\frac{a^m}{a^n}=a^{m-n}$.

When we apply this property, the expression will be,

$=12\times a^{7-6} \times b^{9-12} c^{17-3}$

$=12\times a^1 \times b^{-3} c^{14}$

We rewrite this as a positive index to get,

$=\frac{12ac^{14}}{b^3}$

The correct answer is C

Answer 2

The answer is c. 12ac^14/b^3