Exponents and their rules

Fractional exponent is also called as a rational exponent which is in the form of a fraction like ½ (square root), ⅓ (cube root), ¼ (fourth root) etc.

A fractional exponent with 1/n is the n-th root of the given base.

(a)^ ⅓ = ³√a

A fractional exponent with m/n, we need to take the m-th power of the base and then find the n-th root or vice versa

(a) ^⅔ = ³√a²

The basic exponential rules are as follows: 

Exponents and tLaw of exponents:

1. Any number except zero when raised to zero equals 1
2. Any number raised to 1 equals itself
3. A number with negative power equals its reciprocal with a positive power
4. When we divide terms with same bases, the powers are subtracted
5. When we multiply terms with same bases, the powers are added
6. When a term is raised to a power with a whole power, the powers are multiplied.
7. When product of terms are raised to a power, each term is raised to that power

Subtracting exponents:

When we divide terms with same bases, the exponents are subtracted

The basic exponential rules are as follows: 

For example,

= 3³

Exponent rules:

1. When we multiply terms with same bases, the powers are added

2. When we divide terms with same bases, the powers are subtracted

3. Any number except zero when raised to zero equals 1

4. Any number raised to 1 equals itself

5. When a term is raised to a power with a whole power, the powers are multiplied.

6. When product of terms are raised to a power, each term is raised to that power

7. A number with negative power equals its reciprocal with a positive power

LESSON ON VOLUME OF SOLIDS

Often, students work with shapes and solids under Geometry. Geometry deals with the study of solids and shapes and the measurements associated with them. Therefore various calculations with respect to the size, shape and volume is often done under Geometry. One of such computations is calculating volume of solids.
There are various types of solids. They are:

· Cube

· Cuboid

· Prism

· Pyramid

· Cylinder

· Sphere

· Cone

Students can use various volume formulas to calculate the volume of the various solids. The Volume is basically the 3 dimensional 'space' occupied by a particular solid.

Students can solve problems on finding volume and learn how to find volume of various solids. Ample problems are available online for students to practice upon. They can also get Geometry tutoring online to get help with solving problems in geometry.

how to find the slope

Let us learn how to find the slope

Interpret the slopes of the following lines joining

(i) (6,4) and (−7, 4) (ii) (−2,8) and (−2, 7).

(i) To find Slope of the given line “m”= y₂- y₁ / x₂ – x₁ = 4-4 / -7- 6 = 0 /-13 = 0

∴ Therefore line is parallel to the x-axis.

(ii) To find Slope of the given line “m” = y₂- y₁ / x₂ – x₁ = 7-8 / -2+2 = not defined.

Therefore, The line is perpendicular to the x-axis.

In our next blog we shall learn about blood type personality traits I hope the above explanation was useful.Keep reading and leave your comments.

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final exam calculator

Let us learn about final exam calculator

Final exam score is referred as the calculation of the marks secured by each student that can be used to predict the results of the students & the grades secured by them.
Final exam score includes calculation of the total marks of students, calculation of the percentages & the final step is the prediction of the grade with respect to his/her percentage.
Final exam score calculator is mostly used in the educational institutions to predict the grading of their students & the grading system often requires the final percentage of score of the students. Final exam calculator helps tutors to calculate score which helps the institutions to know the ranking of their university according to their pass percentage of the students.

In our next blog we shall learn about oxygen properties I hope the above explanation was useful.Keep reading and leave your comments.

standard deviation table

Let us learn about standard deviation table

Standard deviation table, a standard normal table also known as the "Unit Normal Table" is a math table for the values of Φ, the cumulative distribution function of the normal distribution. Standard deviation table are used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, & by extension, any normal distribution.

Standard deviation table is the measure of describing squared mean difference variability & spread of the Data set in the given total numbers. Standard deviation table is used to take the measurement of taking square root and average of numbers in the Data set.

Formula for standard deviation,

In our next blog we shall learn about stationary waves I hope the above explanation was useful.Keep reading and leave your comments.

logarithm solver

Let us solve problem using logarithm solver

Solve for x: 5^x = 2.
Apply the logarithm of both sides.
log 5^x = log 2
Use theorem 2 to simplify the equation.
x * log 2 = log 5
Solve for x by dividing each side by log three
x = (log 5/log 2)
A decimal approximation may be found if desired -
x = 2.32192809.
Solve Log₃(2x+5) = 2 for x.
Write an equivalent exponential expression, 2x+5= 3²
2x+5=3*3
2x+5=9
Solve for x. 2x=4, x = 2.
In our next blog we shall learn about what is naoh I hope the above explanation was useful.Keep reading and leave your comments.

equivalent fractions calculator

Let us solve problem using equivalent fractions calculator

Convert 9.6 to equivalent fraction number by using equivalent fractions calculator
Here transfer 9.6 to an equivalent fraction,
Multiply both the numerator & the denominator by 10.
= (9.6 x 10)/10
= 96/10
Hence there is one digit in a place of the very last digit is the "10th" decimal place. Therefore we can just say that 0.1 is the same as 1/10.
= 9.6 can be written as the equivalent fraction = 96/10

In our next blog we shall learn about refractive index of glass I hope the above explanation was useful.Keep reading and leave your comments.