Question

2-⁴x15-³x635/5²x10-⁴

simplify and write in exponential form. ​

Answer 1

QUESTION:

$\sf\dfrac{2^{-4}\times15^{-3}\times625}{5^2\times10^{-4}}$

ANSWER:

To Simplify:

$\sf\dfrac{2^{-4}\times15^{-3}\times625}{5^2\times10^{-4}}$

Solution:

We are given that,

$:\implies\sf\dfrac{2^{-4}\times15^{-3}\times625}{5^2\times10^{-4}}$

So,

$:\implies\sf\dfrac{2^{-4}\times(3\times5)^{-3}\times(5\times5\times5\times5)}{5^2\times(2\times5)^{-4}}$

So,

$:\implies\sf\dfrac{2^{-4}\!\!\!\!\!\!\!\!\!\bigg/\:\times3^{-3}\times5^{-3}\times5^4}{5^2\times2^{-4}\!\!\!\!\!\!\!\!\!\bigg/\:\times5^{-4}}$

We know that,

$:\implies\sf a^x\times a^y=a^{x+y}$

So,

$:\implies\sf\dfrac{3^{-3}\times5^{-3+4}}{5^{2-4}}$

Hence,

$:\implies\sf\dfrac{3^{-3}\times5^{1}}{5^{-2}}$

We know that,

$:\implies\sf\dfrac{a^x}{a^y}=a^{x-y}$

So,

$:\implies\sf3^{-3}\times5^{1-(-2)}$

$:\implies\sf3^{-3}\times5^{1+2}$

Hence,

$:\implies\sf3^{-3}\times5^3$

Therefore,

$:\implies\bf\dfrac{5^3}{3^3}$

Or

$:\implies\bf\left(\dfrac{5}{3}\right)^3$

Formulae Used:

$\:\:\:\:\bullet\:\:\:\:\sf a^x\times a^y=a^{x+y}$

$\:\:\:\:\bullet\:\:\:\:\sf\dfrac{a^x}{a^y}=a^{x-y}$

Learn More:

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