MCQ
$\Big(\frac{2}{3}\Big)^{-5}$ is equal to:
- A$\Big(\frac{-2}{3}\Big)^5$
- ✓$\Big(\frac{3}{2}\Big)^5$
- C$\frac{2\text{x}-5}{3}$
- D$\frac{2}{3\times5}$
✓
Answer
Correct option: B.
$\Big(\frac{3}{2}\Big)^5$
Rearrange $\Big(\frac{2}{3}\Big)^{-5}$ to get a positive exponent.
$\Big(\frac{2}{3}\Big) ^{-5}=\frac{1}{\big(\frac{2}{3}\big)^5}$
$=\frac{1}{2^5}$
$=\frac{\frac{3^5}{2^5}}{3^5}$
$=\frac{3^5}{2^5}$
$=\Big (\frac{3}{2}\Big)^5$
$\Big(\frac{2}{3}\Big) ^{-5}=\frac{1}{\big(\frac{2}{3}\big)^5}$
$=\frac{1}{2^5}$
$=\frac{\frac{3^5}{2^5}}{3^5}$
$=\frac{3^5}{2^5}$
$=\Big (\frac{3}{2}\Big)^5$
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
The sum of angles of a concave quadrilateral is:
The following pie chart represents the distribution of proteins in parts of a human body. What is the ratio of distribution of proteins in the muscles to that of proteins in the bones?
Which of the following Pythagorean triplet has the smallest member $‘8’$.
→A pie chart (as shown below) represents 45 people's choice, then the number of people who like bananas, is
8 persons can stay in a cubical room. Each person requires 27 $m ^3$ of air. The side of the cube is
→Tick $(\checkmark)$ the correct answer in the following: In an examination, $65\%$ of the total examinees passed. If the number of failures is $420,$ the total number of examinees is.
→Tick $(\checkmark)$ the correct answer in the following: $0.05$ is what percent of $20$?
→The point $(-2, -2)$ is:
→Which of the following has its area and perimeter numerically equal$?$
→Tick $(\checkmark)$ the correct answer in the following: The compound interest on $Rs. 4000$ at $10\%$ per annum for $2$ years $3$ months, compounded annually, is.
→