Question

find value of (1/125)^-2/3 + (1/216)^-4/3

Answer 1

Answer:

answer right or wrong write on comment box

Answer 2

Answer:

$\frac{25}{1296}$ is the required value of  $(\frac{1}{125})^{\frac{-2}{3} }$ ÷ $(\frac{1}{216})^{\frac{-4}{3} }$

Step-by-step explanation:

Explanation:

Given that, $(\frac{1}{125})^{\frac{-2}{3} }$ ÷ $(\frac{1}{216})^{\frac{-4}{3} }$

This can be written as, $(\frac{1}{5^3})^{\frac{-2}{3} }$ ÷ $(\frac{1}{6^3})^{\frac{-4}{3} }$

Now, as we know the exponent rule $(a^m)^n = a^{mn}$

Where $(a^m)^n = m^mn$ is the power rule for exponents  Multiply the exponent by the power to raise a number with an exponent to that power.

Step 1:

We have, s, $(\frac{1}{5^3})^{\frac{-2}{3} }$ ÷ $(\frac{1}{6^3})^{\frac{-4}{3} }$

As we know the power rule for exponent  $(a^m)^n = a^{mn}$.

⇒ $(\frac{1}{5})^{3. \frac{-2}{3} }$ ÷ $(\frac{1}{6})^{3.\frac{-4}{3} }$

⇒ $(\frac{1}{5})^{-2}$ ÷ $(\frac{1}{6})^{-4}$

This can be written as,

⇒$(5)^{2}$ ÷ $(6)^{4}$

⇒$\frac{5^2}{6^4}$ = $\frac{25}{1296}$

[Where $5^2$ = 5 ×  5 = 25 and $6^4$ = 6×6×6×6 = 1296]

Final answer:

Hence, $\frac{25}{1296}$ is the required value of  $(\frac{1}{125})^{\frac{-2}{3} }$ ÷ $(\frac{1}{216})^{\frac{-4}{3} }$

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