Question

Find the value of (5x⁶) × (−1.5x²y³) × (−12xy²) when x = 1, y = 0.5.

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:

\[\left( 5 x^6 \right) \times \left( - 1 . 5 x^2 y^3 \right) \times \left( - 12x y^2 \right)\]

\[ = \left\{ 5 \times \left( - 1 . 5 \right) \times \left( - 12 \right) \right\} \times \left( x^6 \times x^2 \times x \right) \times \left( y^3 \times y^2 \right)\]

\[ = \left\{ 5 \times \left( - 1 . 5 \right) \times \left( - 12 \right) \right\} \times \left( x^{6 + 2 + 1} \right) \times \left( y^{3 + 2} \right)\]

\[ = 90 x^9 y^5 \]

\[\therefore\] \[\left( 5 x^6 \right) \times \left( - 1 . 5 x^2 y^3 \right) \times \left( - 12x y^2 \right) = 90 x^9 y^5\]

Substituting x = 1 and y = 0.5 in the result, we get:

\[90 x^9 y^5 \]

\[ = 90 \left( 1 \right)^9 \left( 0 . 5 \right)^5 \]

\[ = 90 \times 1 \times 0 . 03125\]

\[ = 2 . 8125\]

Thus, the answer is 2.8125.