Find the product. 3 (i): (a2) × (2a22) × (4a26) 3 (ii): (2/3xy) × (−9/10x2y2) 3 (iii): (−10/3pq3) × (6/5p3q)

Question

ScanSolve AI Tutor · Accepted Answer

Here is the solution for the 3rd question:

3. Find the product.

Multiply the numerical coefficients and the variables separately.
$$ (1 \times 2 \times 4) \times (a^2 \times a^{22} \times a^{26}) $$
Multiply the coefficients and add the exponents of the variable $a$ .
$$ 8 \times a^{(2+22+26)} $$ $$ = \boxed{8a^{50}} $$
- 3 (ii): $(\frac{2}{3}xy) \times (-\frac{9}{10}x^2y^2)$

$$
\left(\frac{2}{3}\right) \times \left(-\frac{9}{10}\right)
$$

Multiply the variables by adding their exponents.
$$ x^{(1+2)}y^{(1+2)} $$
Simplify the product of the coefficients and combine with the variables.
$$ -\frac{2 \times 9}{3 \times 10}x^3y^3 = -\frac{18}{30}x^3y^3 $$
Reduce the fraction to its simplest form.
$$ = \boxed{-\frac{3}{5}x^3y^3} $$
- 3 (iii): $(-\frac{10}{3}pq^3) \times (\frac{6}{5}p^3q)$

$$
\left(-\frac{10}{3}\right) \times \left(\frac{6}{5}\right)
$$

Multiply the variables by adding their exponents.
$$ p^{(1+3)}q^{(3+1)} $$
Simplify the product of the coefficients and combine with the variables.
$$ -\frac{10 \times 6}{3 \times 5}p^4q^4 = -\frac{60}{15}p^4q^4 $$
Reduce the fraction to its simplest form.
$$ = \boxed{-4p^4q^4} $$
- 3 (iv): $x \times x^2 \times x^3 \times x^4$
Add the exponents of the variable $x$ .
Remember that $x$ is $x^1$ . $x^{(1+2+3+4)}$
Perform the addition.
$$ = \boxed{x^{10}} $$

Find the product. 3 (i): (a2) x (2a22) x (4a26) 3 (ii): ((2)/(3)xy) x (-(9)/(10)x2y2) 3 (iii): (-(10)/(3)pq3) x ((6)/(5)p3q)