Question
$\frac{-3^{100}}{5}=\frac{-3^{100}}{-5^{100}}$
✓
Answer
$\Big(\frac{-3}{5}\Big)=\Big(\frac{-1\times3}{5}\Big)^{100}$
$\big[\because-3=1\times3\big]$
$\frac{(-1)^{100}\times3^{100}}{5^{100}}$
$\big[\because(\text{a}\times\text{b}^{\text{m}})=\text{a}^{\text{m}}\times\text{b}^{\text{m}}\big]$
$\frac{1\times3^{100}}{5^{100}}$
$\big[\because(-1)^{\text{n}}=1,\text{ if }\text{n}\text{ is even}\big]$
$\frac{3^{100}}{5^{100}}$
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, $\frac{-3^{100}}{-5^{100}}=\frac{3^{10}}{5^{100}}$
$\big[\because-3=1\times3\big]$
$\frac{(-1)^{100}\times3^{100}}{5^{100}}$
$\big[\because(\text{a}\times\text{b}^{\text{m}})=\text{a}^{\text{m}}\times\text{b}^{\text{m}}\big]$
$\frac{1\times3^{100}}{5^{100}}$
$\big[\because(-1)^{\text{n}}=1,\text{ if }\text{n}\text{ is even}\big]$
$\frac{3^{100}}{5^{100}}$
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.
Explore more
Similar questions
In Fig. a transversal $n$ cuts two lines $l$ and $m$. If $\angle 1=70^{\circ}$ and $\angle 7=80^{\circ}$, is $l \| m$ ?
→$1$ lakh $= 10 $_____.
→Simplify: $(-4)^3$
→Fill in the blanks: $7 \times (-3) = (-3) \times ($____$)$
→Name the pairs of angles in each figure.
Write the statement in the form of algebraic expressions and write whether it is monomial, binomial or trinomial Area of a square with side $x.$
→Find
$1 \frac{4}{9} \times 6$
→$1 \frac{4}{9} \times 6$
3x + 23x2 + 6y2 + 2x + y2 + ____________ = 5x + 7y2.
The net given below in Fig can be used to make a cube.
$1.$ Which edge meets $AN?$
$2.$ Which edge meets $DE?$
→$1.$ Which edge meets $AN?$
$2.$ Which edge meets $DE?$
Copy the figure with punched holes and find the axes of symmetry:
