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1
If
sqrt(32x^(5)y^(6)) is equal to
ax^(b)y^(c)sqrt(dx), what is the value of
ac ?

$1$ $\newline$ If $\sqrt{32 x^{5} y^{6}}$ is equal to $a x^{b} y^{c} \sqrt{d x}$ , what is the value of $a c$ ?

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Evaluate expression when two complex numbers are given

Full solution

Q.

1

\newline

If

\sqrt{32 x^{5} y^{6}}

is equal to

a x^{b} y^{c} \sqrt{d x}

, what is the value of

a c

?

Simplify Expression: We need to simplify $\sqrt{32x^{5}y^{6}}$ first. $\newline$ $\sqrt{32x^{5}y^{6}} = \sqrt{32} \cdot \sqrt{x^{5}} \cdot \sqrt{y^{6}}$ $\newline$ $= 4 \cdot \sqrt{2} \cdot x^{\frac{5}{2}} \cdot y^{3}$
Compare with Given Format: Now let's compare it to $ax^{b}y^{c}\sqrt{dx}$ . We have $4 \cdot \sqrt{2} \cdot x^{\frac{5}{2}} \cdot y^{3} = ax^{b}y^{c}\sqrt{dx}$ . So, $a = 4 \cdot \sqrt{2}$ , $b = \frac{5}{2}$ , $c = 3$ , and $d = 2$ .
Find $ac$ : To find $ac$ , we multiply $a$ and $c$ . $ac = (4 \times \sqrt{2}) \times 3 = 12 \times \sqrt{2}$

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