Question

Class 8
explain it don't write single answer​

Answer 1

Answer to your question is in the attachment

Hope this helps

Answer 2

Answer:

1= $\mathrm{Simplify}\:\left(\frac{2^5}{2^8}\right)^2\cdot \:2^{-5}:\quad \frac{1}{2048}\quad \left(\mathrm{Decimal:\quad }\:0.00048\dots \right)$

Steps

$\left(\frac{2^5}{2^8}\right)^2\cdot \:2^{-5}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$=\frac{1}{2^5}\left(\frac{2^5}{2^8}\right)^2$

$=\frac{1}{2^6}\cdot \frac{1}{2^5}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{1\cdot \:1}{2^6\cdot \:2^5}$

$=\frac{1}{2^6\cdot \:2^5}$

$=\frac{1}{2^{11}}$

$=\frac{1}{2048}$

$= 2048$

2= $-4^{-3}\cdot \:5^{-3}\cdot \left(-5^3\right)=\frac{1}{64}\quad \left(\mathrm{Decimal:\quad }\:0.015625\right)$

Steps

$-4^{-3}\cdot \:5^{-3}\left(-5^3\right)$

$\mathrm{Apply\:the\:rule}:\quad \:-a\left(-b\right)=ab$

$-4^{-3}\cdot \:5^{-3}\left(-5^3\right)=4^{-3}\cdot \:5^{-3}\cdot \:5^3$

$=4^{-3}\cdot \:5^{-3}\cdot \:5^3$

$=4^{-3}\cdot \:1$

$=4^{-3}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$=\frac{1}{4^3}$

$4^3=64$

$=\frac{1}{64}$

3= $\mathrm{Simplify}\:\frac{1}{8}\cdot \:3^{-3}:\quad \frac{1}{216}\quad \left(\mathrm{Decimal:\quad }\:0.00462\dots \right)$

Steps

$\frac{1}{8}\cdot \:3^{-3}$

$\mathrm{Multiply\:fractions}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}$

$=\frac{1\cdot \:1}{8\cdot \:3^3}$

$\mathrm{Multiply\:the\:numbers:}\:1\cdot \:1=1$

$=\frac{1}{3^3\cdot \:8}$

$=\frac{1}{216}$

4= $-3^4\left(\frac{5}{3}\right)^4=-625$

Steps

$-3^4\left(\frac{5}{3}\right)^4$

$=-3^4\cdot \frac{5^4}{3^4}$

$\mathrm{Multiply\:fractions}:\quad \:a\cdot \frac{b}{c}=\frac{a\:\cdot \:b}{c}$

$=-\frac{5^4\cdot \:3^4}{3^4}$

$\mathrm{Cancel\:the\:common\:factor:}\:3^4$

$=-5^4$

$5^4=625$

$=-625$

Hope it helps you

Eva*