Question

Ch- Indices
Evalute the following
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Answer 1

Answer:

Ch- Indices

Evalute the following

Don't spam

Answer 2

Step-by-step explanation:

Question:-

Simplify:

$\bigg( \frac{64}{125} \bigg) ^{ - \frac{2}{3} } + \frac{1}{ \bigg( \frac{256}{625} \bigg) ^{ \frac{1}{4} } } + \bigg( \frac{ \sqrt{25} }{ \sqrt[3]{64} } \bigg)^{0}$

Solution:-

Let's solve the problem

we have,

$\bigg( \frac{64}{125} \bigg) ^{ - \frac{2}{3} } + \frac{1}{ \bigg( \frac{256}{625} \bigg) ^{ \frac{1}{4} } } + \bigg( \frac{ \sqrt{25} }{ \sqrt[3]{64} } \bigg)^{0}$

$⟹ \left\{ \bigg( \frac{4}{5} \bigg) ^{ \cancel{3}} \right\}^{ - \frac{2}{ \cancel{3}} } + \frac{1}{\left\{ \bigg( \frac{4}{5} \bigg) ^{ \cancel{4}} \right\} ^{ \frac{1}{ \cancel{4}} } } +\left\{{ \frac{( {5}^{ \cancel{2}} )^{ \frac{1}{ \cancel{2}} } }{( {4}^{ \cancel{3}} )^{ \frac{1}{ \cancel{3}} } } }\right\}^{0}$

$⟹ \bigg( \frac{4}{5} \bigg)^{ - 2} + \frac{1}{ \frac{4}{5} } + \bigg( \frac{5}{4} \bigg) ^{0}$

$⟹ \bigg( \frac{5}{4} \bigg)^{2} + \frac{5}{4} + 1$

$⟹ \frac{25}{16} + \frac{5}{4} + 1$

$⟹ \frac{61}{16}$

$⟹3 \frac{13}{16}$

Answer:-

$3 \frac{13}{16}$

:)

Know more:-

Low of Integral Exponents

For any two real numbers a and b, a, b ≠ 0, and for any two positive integers, m and n

➲ If a be any non - zero rational number, then

a^0 = 1

➲ If a be any non - zero rational number and m,n be integer, then

(a^m)^n = a^mn

➲ If a be any non - zero rational number and m be any positive integer, then

a^-m = 1/a^m

➲ If a/b is a rational number and m is a positive integer, then

(a/b)^m = a^m/b^m

➲ For any Integers m and n and any rational number a, a ≠ 0

a^m × a^n = a^m+n

➲ For any Integers m and n for non - zero rational number a,

a^m ÷ a^n = a^m-n

➲ If a and b are non - zero rational numbers and m is any integer, then

(a+b)^m = a^m × b^m

I hope it's help you...☺