Maths-
General
Easy
Question
Evaluate:
a−3b−4 / a−2b−3
Hint:
In Mathematics, lets say, "a" represents a number and "n" is the number of times that number is to be multiplied with itself, in order to get a desired result. Then, such result can be written as an, where a is called the base and n is its power/ exponent.
an = a × a × ... × a n times.
The correct answer is: Simplifying the given expression, we get the value 1/ab.
Step-by-step solution:-
a−3b−4 / a−2 b−3
= a-3-(-2) × b-4-(-3) ….......................................................... (an/am = an-m)
= a-3+2 × b-4+3
= a-1 × b-1
= 1/a × 1/b …................................................................ (b-n = 1/bn)
= 1/ab
Final Answer:-
∴ Simplifying the given expression, we get the value 1/ab.
Related Questions to study
Maths-
Prove that ∠BAC ≅ ∠CAD
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)
Prove that ∠BAC ≅ ∠CAD
![](data:image/png;base64,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)
Maths-General
Maths-
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Express the following recurring decimals as vulgar fraction
a) 0.444444444
Maths-General
Maths-
(32)3 + (2/3)0 + 35 × (1/3)4
(32)3 + (2/3)0 + 35 × (1/3)4
Maths-General
Maths-
Express 0.5248 in the lowest form.
Express 0.5248 in the lowest form.
Maths-General
Maths-
Write the following numbers in the scientific notation : 0.00000000065
Write the following numbers in the scientific notation : 0.00000000065
Maths-General
Maths-
Write the following numbers in the scientific notation : a) 5,07,460000000
Write the following numbers in the scientific notation : a) 5,07,460000000
Maths-General
Maths-
A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?
A town has about 25,00 people living in it and the mayor wants to send each person 10,00 as a celebration gift because the town won the Federal Lottery for Small Towns. How much money would the town need to give out this celebration gift?
Maths-General
Maths-
The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?
The temperature halfway to the Sun from venus is approximately 1,800° c and scientists theorize that it may be up to 26,000 times hotter at the center of the Sun. Approximately how hot is it at the center of the Sun?
Maths-General
Maths-
A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?
A state has an area of approximately 9,604,100,000 square miles and has approximately 110,000 people. How much area is this per person?
Maths-General
Maths-
Convert the following fractions to repeating decimals
d) ![1 over 6](data:image/png;base64,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)
Convert the following fractions to repeating decimals
d) ![1 over 6](data:image/png;base64,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)
Maths-General
Maths-
Convert the following fractions to repeating decimals
c) ![10 over 33](data:image/png;base64,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)
Convert the following fractions to repeating decimals
c) ![10 over 33](data:image/png;base64,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)
Maths-General
Maths-
Convert the following fractions to repeating decimals
b) ![7 over 18](data:image/png;base64,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)
Convert the following fractions to repeating decimals
b) ![7 over 18](data:image/png;base64,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)
Maths-General
Maths-
Convert the following fractions to repeating decimals
a) ![11 over 12](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAjCAYAAACHIWrsAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAALFJREFUeNpjYMAP1IC4FogvUEkdQbAYiNOA+D+V1BEN/lNZ3aiFoxaOWjiILfyPBVOibhSMAuqnSGriUTAKaAMINf+sgXgNEH8C4l9QddG0bCYeBOJIIOaB8rWA+ChUjC7VEwjIA/EleloIAj/oaaElNFjpYiEHEJ+EJiaaWygIxBuA2I0ebRolqGUq9GhEaQDxbCDmonbVhQ2IA/EqIGahRV2JDWyB+pCmlTKxlTZWAAB+VmHzTK3WnQAAAGR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWZyYWM+PG1uPjExPC9tbj48bW4+MTI8L21uPjwvbWZyYWM+PC9tYXRoPieYCYcAAAAASUVORK5CYII=)
Convert the following fractions to repeating decimals
a) ![11 over 12](data:image/png;base64,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)
Maths-General
Maths-
Convert the following repeating decimals to fractions
d) 3.25252525252...............
Convert the following repeating decimals to fractions
d) 3.25252525252...............
Maths-General
Maths-
Convert the following repeating decimals to fractions
c) 0.2151515151515........
Convert the following repeating decimals to fractions
c) 0.2151515151515........
Maths-General