Question

if x/y= (3/2)²÷(5/7)⁰ find the value of ( y/ x )³​

Answer 1

the answer will be

2/3 the whole raise to 6

(2/3)⁶ = 64/729

Answer 2

$\bf \bigg( { \frac{y}{x} \bigg) }^{3} = { \frac{64}{729} }$

Given:

• $\frac{x}{y} = \frac{ {( \frac{3}{2} )}^{2} }{( { \frac{5}{7} )}^{0} }$

To find:

• Find the value of $\bigg( \frac{y}{x} \bigg)^{3}$

Solution:

Identity to be used:

1. ${a}^{0} = 1$
2. $( { {x}^{n} })^{m} = {x}^{nm}$
3. $\frac{a}{b} = \frac{x}{y}$ then $\frac{b}{a} = \frac{y}{x}$

Step 1:

Simplify the given expression.

$\frac{x}{y} = \frac{ { \big( \frac{3}{2} \big)}^{2} }{1 }$

or

$\frac{x}{y} = \bigg( { \frac{3}{2} \bigg)}^{2}$

Step 2:

Write the reciprocal.

$\frac{y}{x} = \bigg( { \frac{2}{3} \bigg)}^{2}$

Step 3:

Cube both sides of equation.

$\bigg( { \frac{y}{x} \bigg) }^{3} = \bigg( { \bigg ({ \frac{2}{3} \bigg)}^{2} \bigg )}^{3}$

or

$\bigg( { \frac{y}{x} \bigg) }^{3} = \bigg({ \frac{2}{3} \bigg)}^{6}$

or

$\bigg( { \frac{y}{x} \bigg) }^{3} = { \frac{64}{729} }$

Thus,

$\bf \bigg( { \frac{y}{x} \bigg) }^{3} = { \frac{64}{729} }$

Learn more:

1) On Simplifying 8^3×2^4, we get. (a) 16^7 (b) 2^10 (c) 2 ^13 (d) 8^4

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2) Find the value of 8x 3 +27y 3 , if 2x+3y =8 and xy =2

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