Question

(2/3)^-5 is equal to ____________
Kindly tell me I will make you brain list

Answer 1

Question:-

(2/3)^-5 is equal to ____________

${\red{\underline{\underline{\bold{Answer:-}}}}}$

(2/3)^-5

(2/3)^-5

firstly we make the power positive

to make the power positive we can use multiplicative inverse

so , (2/3)^-5 = (3/2)^5

hence , 3×3×3×3×3/2×2×2×2×2

= 243/32

so , (2/3)^-5 equal to 243/32 or (3/2)^5

hope it helps you..

Answer 2

Question:-

Find the value of :-${ (\frac{2}{3}) }^{ - 5}$

${\green{\underline{\underline{\bold{Solution:-}}}}}$

we know that

${a}^{ - n} = { (\frac{1}{a}) }^{n}$

${ (\frac{2}{3}) }^{ - 5} = { \frac{3}{2} }^{5} \\ \\ = \frac{3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} = \frac{243}{32}$

_______________

Identities used here:-

• ${a}^{-n}={(\frac{1}{a})}^{n}$

_______________

Additional Identities:-

• ${a}^{m} \times {a}^{n} = {a}^{m + n}$

• $\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$ If m>n

• $\frac{ {a}^{m} }{ {a}^{n} } = \frac{1}{ {a}^{n - m} }$ [If n>m]

• ${a}^{0} = 1$ [For any value of a]

• ${a}^{1} = a$ [ For any value of a]