Download App

Exponents Of Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsExponents Of Real Numbers4 Marks
Question
Simplify:$\Big(\frac{\text{x}^{\text{a}+\text{b}}}{\text{x}^\text{c}}\Big)^{\text{a}-\text{b}}\Big(\frac{\text{x}^{\text{b}+\text{c}}}{\text{x}^\text{a}}\Big)^{\text{b}-\text{c}}\Big(\frac{\text{x}^{\text{c}+\text{a}}}{\text{x}^\text{b}}\Big)^{\text{c}-\text{a}}$
✓

Answer

$\Big(\frac{\text{x}^{\text{a}+\text{b}}}{\text{x}^\text{c}}\Big)^{\text{a}-\text{b}}\Big(\frac{\text{x}^{\text{b}+\text{c}}}{\text{x}^\text{a}}\Big)^{\text{b}-\text{c}}\Big(\frac{\text{x}^{\text{c}+\text{a}}}{\text{x}^\text{b}}\Big)^{\text{c}-\text{a}}$$=\big(​​\text{x}^{\text{a}+\text{b}+\text{c}}\big)^{\text{a}-\text{b}}\big(\text{x}^{\text{b}+\text{c}+\text{a}}\big)^{\text{b}-\text{c}}\big(\text{x}^{\text{c}+\text{a}-\text{b}}\big)^{\text{c}-\text{a}}$
$=\text{x}^{(\text{a}-\text{b})(\text{a}+\text{b}-\text{c})}\times\text{x}^{(\text{b}-\text{c})(\text{b}+\text{c}-\text{a})}\times\text{x}^{(\text{c}-\text{a})(\text{c}+\text{a}-\text{b})}$
$=\text{x}^{\text{a}^\text{2}+\text{ab}-\text{ac}-\text{ab}-\text{b}^\text{2}+\text{bc}}\times\text{x}^{\text{b}^\text{2}+\text{bc}-\text{ab}-\text{bc}-\text{c}^2+\text{ac}}\times\text{x}^{\text{c}^2+\text{ac}-\text{bc}-\text{ac}-\text{a}^\text{2}+\text{ab}}$
$=\text{x}^{\text{a}^2-\text{ac}-\text{b}^2+\text{bc}}\times\text{x}^{\text{b}^2-\text{ab}-\text{c}^2+\text{ac}}\times\text{x}^{\text{c}^2-\text{bc}-\text{a}^2+\text{ab}}$
$=\text{x}^{\text{a}^2-\text{ac}-\text{b}^2+\text{bc}+\text{b}^2-\text{ab}-\text{c}^2+\text{ac}+\text{c}^2-\text{bc}-\text{a}^2+\text{ab}}$
$=\text{x}^0$
$=1$

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 "4 Mark Question" from Exponents Of Real Numbers→Exponents Of Real Numbers — all question types→Maths STD 9 question papers→Maharashtra Board STD 9 question papers→Maharashtra Board question paper generator→

Similar questions

In the figure given below, AB || CD. Find the value of x in each case.

→
Prove that if the two arms of an angle are perpendicular to the two arms of another angle, then the angles are either equal or supplementary.
→
Plot the following points on the graph paper:(0, 0)
→
If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?
→
In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays. Find the probability that a ball played:
  1. He hit boundary
  2. He does not hit a boundary.
→
In the given figure, line AB || line CD and line PQ is transversal. Measure of one of the angles is given. Hence find the measures of the following angles.

i. ∠ART
ii. ∠CTQ
iii. ∠DTQ
iv. ∠PRB
→
The monthly maximum temperature of a city is given in degree Celsius in the following data. By taking suitable classes, prepare the grouped frequency distribution table
29.2, 29.0, 28.1, 28.5, 32.9, 29.2, 34.2, 36.8, 32.0, 31.0, 30.5, 30.0, 33, 32.5, 35.5, 34.0, 32.9, 31.5, 30.3, 31.4, 30.3, 34.7, 35.0, 32.5, 33.5.29.0. 29.5.29.9.33.2.30.2
From the table, answer the following questions.
i. For how many days the maximum temperature was less than 34°C?
ii. For how many days the maximum temperature was 34°C or more than 34°C?
→
Read the bar graph given in figure and answer the following questions:
  1. What information does it give?
  2. In which part the expenditure on education is maximum in 1980?
  3. In which part the expenditure has gone up from 1980 to 1990?
  4. In which part the gap between 1980 and 1990 is maximum?
→
For any positive real number x, write the value of $\big\{(\text{x}^\text{a})^\text{b}\big\}^{\frac{1}{\text{ab}}}\big\{(\text{x}^\text{b})^\text{c}\big\}^{\frac{1}{\text{bc}}}\big\{(\text{x}^\text{c})\text{a}\big\}^{\frac{1}{\text{ca}}}$
→
The height of a right circular cylinder is $10.5m$. Three times the sum of the areas of its two circular faces is twice the area of the curved surface.
Find the volume of the cylinder.
→