Evaluate: (64 125 )^ -2 3 + (256 625 )^ -1 4 + (3 7 )^0 - Vidyadip

Question

Evaluate:
$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$

✓

Answer

$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$
$\Big(\frac{125}{64}\Big)^{\frac{2}{3}}+\Big(\frac{625}{256}\Big)^{\frac{1}{4}}+1$
$=\Big(\frac{5^3}{4^3}\Big)^{\frac{2}{3}}+\Big(\frac{5^4}{4^4}\Big)^{\frac{1}{4}}+1$
$=\frac{5^{3\times\frac{2}{3}}}{4^{3\times\frac{2}{3}}}+\frac{5^{4\times\frac{1}{4}}}{4^{4\times\frac{1}{4}}}+1$
$=\frac{5^2}{4^2}+\frac{5}{4}+1$
$=\frac{25}{16}+\frac{5}{4}+1$
$=\frac{25+20+16}{16}$
$=\frac{61}{16}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Presentation of Data in Tabular Form→Presentation of Data in Tabular Form — all question types→Maths STD 9 question papers→Gujarat Board STD 9 question papers→Gujarat Board question paper generator→

Similar questions

Prove that:
$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\frac{1}{\Big(\frac{256}{625}\Big)^{\frac{1}{4}}}+\frac{\sqrt{25}}{\sqrt[3]{64}}=\frac{65}{16}$

If 9x²+ 25y²= 181 and xy = -6, find the value of 3x + 5y.

Express the following decimals in the form $\frac{\text{p}}{\text{q}},$ where p, q are integers and $\text{q}\neq0.$
$32.12\overline{35}$

Show that the angles of an equilateral triangle are 60° each.

Factorize:
7(x - 2y)² - 25(x - 2y) + 12

If the mean of the following data is 20.2, find the value of p:

x	10	15	20	25	30
f	6	8	p	10	6

A circus tent is cylindrical to a height of 3 metres and conical above it. If its diameter is 105m and the slant height of the conical portion is 53m, calculate the length of the canvas 5m wide to make the required tent. $\Big(\text{Use}\ \pi=\frac{22}{7}\Big).$

ABC and ADC are two right triangles with common hypotenuse AC. Prove that $\angle C A D = \angle C B D.$

If x is a positive real number and exponents are rational numbers, simplify
$\Big(\frac{\text{x}^\text{b}}{\text{x}^\text{c}}\Big)^{\text{b+c-a}}\times\Big(\frac{\text{x}^\text{c}}{\text{x}^\text{a}}\Big)^{\text{c+a-b}}\times\Big(\frac{\text{x}^\text{a}}{\text{x}^\text{b}}\Big)^{\text{a+b-c}}.$

A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625m³. If the present depth of water is 1.3m, find the volume of water already used from the tank.