Question
Prove that:
$\bigg[7\Big\{(81)^\frac{1}{4}+(256)^\frac{1}{4}\Big\}^\frac{1}{4}\bigg]^4=16807$
$\bigg[7\Big\{(81)^\frac{1}{4}+(256)^\frac{1}{4}\Big\}^\frac{1}{4}\bigg]^4=16807$
✓
Answer
$\text{L.H.S}=\bigg[7\Big\{(81)^\frac{1}{4}+(256)^\frac{1}{4}\Big\}^\frac{1}{4}\bigg]^4=16807$
$=\bigg[7\Big\{3^{4\times\frac{1}{4}}+4^{4\times\frac{1}{4}}\Big\}^\frac{1}{4}\bigg]^4$
$=\bigg[7\big\{3+4\big\}^\frac{1}{4}\bigg]^4$
$=\Big[7\big\{7\big\}^\frac{1}{4}\Big]^4$
$=7^4\times7^{\frac{1}{4}\times4}$
$=7^4\times7$
$=7^5$
$=16807$
$=\text{R.H.S.}$
$=\bigg[7\Big\{3^{4\times\frac{1}{4}}+4^{4\times\frac{1}{4}}\Big\}^\frac{1}{4}\bigg]^4$
$=\bigg[7\big\{3+4\big\}^\frac{1}{4}\bigg]^4$
$=\Big[7\big\{7\big\}^\frac{1}{4}\Big]^4$
$=7^4\times7^{\frac{1}{4}\times4}$
$=7^4\times7$
$=7^5$
$=16807$
$=\text{R.H.S.}$
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
Write the coordinates of each of the points P, Q, R, S, T and O from the:
Find the median of the data:
12, 17, 3, 14, 5, 8, 7, 15
12, 17, 3, 14, 5, 8, 7, 15
Evaluate:
$\Big(\frac{81}{16}\Big)^{-\frac{3}{4}}\Big[\Big(\frac{25}{9}\Big)^{-\frac{3}{2}}\div\Big(\frac{5}{2}\Big)^{-3}\Big]$
→$\Big(\frac{81}{16}\Big)^{-\frac{3}{4}}\Big[\Big(\frac{25}{9}\Big)^{-\frac{3}{2}}\div\Big(\frac{5}{2}\Big)^{-3}\Big]$
Find the values of x in each of the following:
→$\Big(\frac{3}{5}\Big)^\text{x}\Big(\frac{5}{3}\Big)^{2\text{x}}=\frac{125}{27}$
The diameters of two cones are equal. If their slant height are in the ratio 5 : 4, find the ratio of their curved surfaces.
A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table:
Find the probability:
| Monthly income (in Rs.) | Number of Televisions/ household | |||
| 0 | 1 | 2 | Above 2 | |
| <10000 10000-14999 15000-19999 20000-24999 25000 and above | 20 10 0 0 0 | 80 240 380 520 1100 | 10 60 120 370 760 | 0 0 30 80 220 |
- Of a household earning Rs. 10000 - Rs 14999 per year and having exactly one television.
- Of a household earning Rs. 25000 and more per year and owning 2 televisions.
- Of a household not having any television.
Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where p, q are integers and $\text{q}\neq0.$
$0.00\overline{32}$
→$0.00\overline{32}$
Rationalise the denominator of the following:
$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$
→$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$
The table given below shows the marks obtained by 30 students in a test.
Out of these students, one is chosen at random. What is the probability that the marks of the chosen student:
| Marks (Class interval) | 1 - 10 | 11 - 20 | 21 - 30 | 31 - 40 | 41 - 50 |
| Number of students (Frequency) | 7 | 10 | 6 | 4 | 3 |
- Are 30 or less?
- Are 31 or more?
- Lie in the interval 21 - 30?
In Fig. AB || DE Find $\angle\text{ACD}.$
→