Question

Evaluate (3.2x⁶y³) × (2.1x²y²) when x = 1 and y = 0.5.

Answer 1

First multiply the expressions and then substitute the values for the variables.
To multiply algebric experssions use the commutative and the associative laws along with the law of indices, \[a^m \times a^n = a^{m + n}\].

We have,

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

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

\[ = 6 . 72 x^8 y^5 \]

Hence,

\[\left( 3 . 2 x^6 y^3 \right) \times \left( 2 . 1 x^2 y^2 \right) = 6 . 72 x^8 y^5\]

Now, substitute 1 for x and 0.5  for y in the result.

\[6 . 72 x^8 y^5 \]

\[ = 6 . 72 \left( 1 \right)^8 \left( 0 . 5 \right)^5 \]

\[ = 6 . 72 \times 1 \times 0 . 03125\]

\[ = 0 . 21\]

Hence, the answer is \[0 . 21\].