Question

evaluate : (3 power minus 5 into 10 power minus 5 into 5 power 3 ) divided by ( 5 power minus 7 into 6 power minus 5 into 5 power 5 )​

Answer 1

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Answer 2

$\dfrac{3^{-5}\times 10^{-5}\times 5^3}{5^{-7}\times 6^{-5}\times 5^5}=1$

Step-by-step explanation:

Given : Expression $\dfrac{3^{-5}\times 10^{-5}\times 5^3}{5^{-7}\times 6^{-5}\times 5^5}$

To find : Evaluate the expression ?

Solution :

$\dfrac{3^{-5}\times 10^{-5}\times 5^3}{5^{-7}\times 6^{-5}\times 5^5}$

Using exponent property,

$a^m\times a^n=a^{m+n}\\ \frac{a^m}{a^n}=a^{m-n}\\(a\times b)^m=a^m\times b^m$

$=\dfrac{3^{-5}\times (2\times 5)^{-5}\times 5^3}{5^{-7+5}\times (3\times 2)^{-5}}$

$=\dfrac{3^{-5}\times 2^{-5}\times5^{-5}\times 5^3}{5^{-2}\times 3^{-5}\times 2^{-5}}$

$=\dfrac{3^{-5}\times 2^{-5}\times5^{-2}}{5^{-2}\times 3^{-5}\times 2^{-5}}$

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

$=3^{0}\times 2^{0}\times 5^{0}$

$=1\times 1\times 1$

$=1$

Therefore, $\dfrac{3^{-5}\times 10^{-5}\times 5^3}{5^{-7}\times 6^{-5}\times 5^5}=1$

#Learn more

2 power 2 × 3power 2 by 2 power -2 × 3 power -1​

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