Question

Which of the following option is equal to $125x^3\times 6^3{y}^3?$

• A. $(6xy{)}^3$
• B. $(5xy{)}^3$
• C. $(30xy{)}^3$
• D. All of the above.

Answer 1

The correct option is C $(30xy{)}^3$

$125x^3\times 6^3{y}^3$
$=5^3{x}^3\times 6^3{y}^3(\because 125=5\times 5\times 5=5^3)$

In the above expression, we can see that exponent of each term is the same, which is $3,$ and the bases are different. So, the multiplication of exponents rule can be defined as
$a^n\times b^n=(a\times b{)}^n=(ab{)}^n,$
which we can use to simplify the given product.

$\therefore$ $5^3{x}^3\times 6^3{y}^3=(5^3\times x^3)\times (6^3\times y^3)=(5x{)}^3\times (6y{)}^3=(5x\times 6y{)}^3=(30xy{)}^3$

$\therefore$ Option (c.) is the correct choice.