Question

2^-5×3^-7×125/15^5×5^-4×6^-8​

Answer 1

Given :

$Expression \dfrac{3^{-5}\times 10^{-7}\times 125}{15^{-5}\times 6^{-7}}$

To find : Simplify the expression ?

Solution :

We can re-write the expression as,

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

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

$Using exponent rule, a^x\times a^y=a^{x+y},\ \frac{a^x}{a^y}=a^{x-y}a$

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

$=3^{7}\times 2^{0}\times 5^{1}=3$

$=2187\times 1\times 5=2187×1×5$

=10935

$Therefore, \dfrac{3^{-5}\times 10^{-7}\times 125}{15^{-5}\times 6^{-7}}=10935$

Hope it helps you

Answer 2

Refer this attachment

Hope it's help you