Gujarat BoardEnglish MediumSTD 7MATHSExponents and Powers1 Mark
Question
$\frac{-3^{100}}{5}=\frac{-3^{100}}{-5^{100}}$
✓
Answer
True. Solution: $\Big(\frac{-3}{5}\Big)=\Big(\frac{-1\times3}{5}\Big)^{100}$$\big[\because-3=1\times3\big]$ $\frac{(-1)^{100}\times3^{100}}{5^{100}}$$\big[\because(\text{a}\times\text{b}^{\text{m}})=\text{a}^{\text{m}}\times\text{b}^{\text{m}}\big]$ $\frac{1\times3^{100}}{5^{100}}$$\big[\because(-1)^{\text{n}}=1,\text{ if }\text{n}\text{ is even}\big]$ $\frac{3^{100}}{5^{100}}$ Now, taking RHS, we have $\frac{-3^{100}}{-5^{100}}=\frac{3^{10}}{5^{100}}$ [$\because$ if both numerator and denominator have negative sign, then it is cacelled out] $\therefore$ LHS = RHS Hence, $\frac{-3^{100}}{-5^{100}}=\frac{3^{10}}{5^{100}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.