Question

answer who know please​

Answer 1

Answer:

5/6

Solution:

The given question is:

$\sf{\dfrac{3^{-7}\times10{-7}\times125}{5^{-5}\times6^{-6}}}$

Now, we can solve this question by following the basic steps as given below:

→ Convert composite numbers to prime numbers by factorising them:

$\sf{=\dfrac{3^{-7}\times5^{-7}\times2^{-7}\times5^{3}}{5^{-5}\times3^{-6}\times2^{-6}}}$

→ Apply the exponential rule, aᵐ ÷ aⁿ = a⁽ᵐ⁻ⁿ⁾ and aᵐ x aⁿ = a⁽ᵐ⁺ⁿ⁾

$\sf{={3^{-1}\times2^{-1}\times5}}$

→ Now, as there are negative exponents, we can use the negative exponent formula which states that to convert a negative exponent to positive, take the reciprocal of the base:

$\sf{=\dfrac{1}{3}\times{\dfrac{1}{2}\times5}}$

→ Multiplying the numerals:

$\sf{\dfrac{5}{6}}$

Hence the required answer is 5/6.

Laws of Exponents:

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

Knowledge Bytes:

→ Negative Exponents Formula

The negative exponents formula states that if you have a number with a negative exponent, take the reciprocal of the base and change the exponent to positive. It can also be done vice-versa.

For example:

$\sf{6^{-2}=\dfrac{1}{36}}$

$\sf{\dfrac{1}{49}=7^{-2}}$

Answer 2

5/6