Question

Evaluate (−8x²y⁶) × (−20xy) for x = 2.5 and y = 1.

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:

\[\left( - 8 x^2 y^6 \right) \times \left( - 20xy \right)\]

\[ = \left\{ \left( - 8 \right) \times \left( - 20 \right) \right\} \times \left( x^2 \times x \right) \times \left( y^6 \times y \right)\]

\[ = \left\{ \left( - 8 \right) \times \left( - 20 \right) \right\} \times \left( x^{2 + 1} \right) \times \left( y^{6 + 1} \right)\]

\[ = 160 x^3 y^7\]

\[\therefore\] \[\left( - 8 x^2 y^6 \right) \times \left( - 20xy \right) = 160 x^3 y^7\]

Substituting x = 2.5 and y = 1 in the result, we get:

\[160 x^3 y^7 \]

\[ = 160 \left( 2 . 5 \right)^3 \left( 1 \right)^7 \]

\[ = 160 \times 15 . 625\]

\[ = 2500\]

Thus, the answer is \[2500\].