Question

Evaluate each of the following when x = 2, y = −1.

\[(2xy) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)\]

Answer 1

To multiply algebraic expressions, we use commutative and associative laws along with the laws of indices, i.e.,​\[a^m \times a^n = a^{m + n}\].

We have:

\[\left( 2xy \right) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right)\]

\[ = \left( 2 \times \frac{1}{4} \right) \times \left( x \times x^2 \times x^2 \right) \times \left( y \times y \times y^2 \right)\]

\[ = \left( 2 \times \frac{1}{4} \right) \times \left( x^{1 + 2 + 2} \right) \times \left( y^{1 + 1 + 2} \right)\]

\[ = \frac{1}{2} x^5 y^4\]

\[\therefore\] \[\left( 2xy \right) \times \left( \frac{x^2 y}{4} \right) \times \left( x^2 \right) \times \left( y^2 \right) = \frac{1}{2} x^5 y^4\]

Substituting x = 2 and y = \[-\] 1 in the result, we get:

\[\frac{1}{2} x^5 y^4 \]

\[ = \frac{1}{2} \left( 2 \right)^5 \left( - 1 \right)^4 \]

\[ = \frac{1}{2} \times 32 \times 1\]

\[ = 16\]

Thus, the answer is 16.