Question

please answer, im desperate​

Answer 1

Question -

Evaluate $\rm( {\frac{ - 1}{27})}^{ - \frac{2}{3} }$

Answer -

$\rm ({\dfrac{ - 1}{27}) }^{ - \frac{2}{3} }$ $\rm = (\dfrac{27}{1})^{ \frac{2}{3} }$

$\rm = ({3}^{3})^\frac{2}{3}$

$\rm = 3 ^{(\cancel3 \times \frac{2}{ \cancel3})}$

$\rm = {3}^{2}$

$\rm = 9$

Additional information -

$\boxed{\sf\gray{ a^m \times a^n = a^{m+n}}}$

$\boxed{\sf\gray {\frac{a^m}{a^n} = a^{m-n}}}$

$\boxed{\sf\gray{ (a^{m)n} = a^{mn} }}$

$\boxed{\sf\gray{ a^{-n} = \frac{1}{a^n}}}$

$\boxed{\sf\gray{ a^{\frac{m}{n}} = \sqrt[n]{a^m}}}$

$\boxed{\sf\gray{(\frac{a}{b})^m = \frac{a^m}{b^m}}}$

where -

$\longrightarrow$a and b are positive real numbers.

$\longrightarrow$m and n are rational numbers.

Answer 2

$\rm\underline\red{Question}$

To find the value of or to Evaluate:-

$\sf⟾({\frac{-1}{27})}^{-\frac{2}{3}}$

$\sf\underline\blue{Solution:-}$

$\sf⟾({\frac{27}{1})}^{\frac{2}{3}}$

$\sf⟾({27)}^{\frac{2}{3}}$

$\sf⟾{3}^{3}{×\frac{2}{3}}$

$\sf⟾{3}^{2}$

$\sf⟾{3×3}$

$\sf⟾{9}$

Therefore,after evaluation of $\bf({\frac{-1}{27})}^{-\frac{2}{3}}$ the result is $\sf{9}$.

Some laws of Exponents.

• $\sf\leadsto{a}^{-n}=\frac{1}{aⁿ}$

• $\sf\leadsto({a}^{m})^{n}={a}^{mn}$

• $\sf\leadsto{a}^{m}×{a}^{n}={a}^{m+n}$

• $\sf\leadsto{\frac{a^m}{aⁿ}}$$\sf={a}^{m-n},a≠0$

• $\sf\leadsto{abⁿ}={aⁿbⁿ}$