Question

2 to the power minus 5 into 15 to the power minus 5 into 500 / 5 to the power minus 6 into 6 to the power minus 5

Answer 1

$\textbf{Given:}$

$\mathsf{\dfrac{2^{-5}{\times}15^{-5}{\times}500}{5^{-6}{\times}6^{-5}}}$

$\textbf{To simplify:}$

$\mathsf{\dfrac{2^{-5}{\times}15^{-5}{\times}500}{5^{-6}{\times}6^{-5}}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\dfrac{2^{-5}{\times}15^{-5}{\times}500}{5^{-6}{\times}6^{-5}}}$

$\mathsf{=\dfrac{2^{-5}{\times}(3{\times}5)^{-5}{\times}5^3{\times}2^2}{5^{-6}{\times}(2{\times}3)^{-5}}}$

$\mathsf{=\dfrac{2^{-5}{\times}3^{-5}{\times}5^{-5}{\times}5^3{\times}2^2}{5^{-6}{\times}2^{-5}{\times}3^{-5}}}$

$\mathsf{=\dfrac{5^{-5}{\times}5^3{\times}2^2}{5^{-6}}}$

$\mathsf{=2^2{\times}5^{(-5+3+6)}}$

$\mathsf{=2^2{\times}5^4}$

$\mathsf{=4{\times}625}$

$\mathsf{=2500}$

$\implies\boxed{\mathsf{\dfrac{2^{-5}{\times}15^{-5}{\times}500}{5^{-6}{\times}6^{-5}}=2500}}$

$\textbf{Find more:}$

Simplify the following

(2-¹×3²/2²×3‐⁴)⁷/²×(2-²×3³/2³×3-⁵)-⁵/²

(ans 12)​

https://brainly.in/question/16527751

Answer 2

Answer:

Hii Mate…

Explanation:

Let us simplify the given expression,

(2-5 × 15 -5 ×500)

(5-6 × 6-5)

= (2-5 × (3×5)-5 ×2² × 5³)

(5-6×(2×3)-5)

=(2−5 × 3-5 ×2² × 5³)

(5-6×2-5×3-5)

=2-5+²-5 ×3-5+5 ×5-5+3-6

=2² × 3°×5⁴

=4×1×625

=2500

Please consider ° sign as 0.

hope it helps.