Question

if 27^r =81 find the value of 27/4 *r^(3r/4)

Answer 1

⇒$27^{r}$ = 81

⇒$(3*3*3)^{r}$= 3⁴

⇒$3^{3r}$ = 3⁴

⇒3r = 4

⇒r=4/3

⇒(27/4)× $r^{3r/4}$

=(27/4)×$4/3^{((3(4/3))/4)}$

=(27/4)×(4/3)

=9

Answer 2

27/4 * r^(3r/4) = 9, where r = 4/3

Step-by-step explanation:

Given,

27ʳ = 81

or, (3³)ʳ = 3⁴

or, 3³ʳ = 3⁴

Equating the exponents, we get

3r = 4

or, r = 4/3

∴ 27/4 * r^(3r/4)

= 27/4 * (4/3)^(3/4 * 4/3)

= 27/4 * (4/3)¹

= 27/4 * 4/3

= 9

Laws of indices:

• aᵇ * aᶜ = aᵇ⁺ᶜ

• aᵇ / aᶜ = aᵇ⁻ᶜ

• aᵖ * bᵖ = (ab)ᵖ

• (aᵇ)ᶜ = aᵇᶜ

Note: To find values of this type of expressions, find the value of the variable from the given conditions and put the value in the expression. Then the problem is solved.