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# Solve the expression: (7/3)(-3)

• Last Updated : 21 Sep, 2021

In mensuration when we have to calculate the area of a square, we simply multiply side by side. This leads to the multiplication of a number with the same number. Suppose there is n rows and in each row, there is a total of ‘n’ element. For the calculation of a total number of elements, we multiply the total number of rows by the number of elements in a row. This is how we introduce the concept of the exponent.

For example,

When we have to add the same number, again and again, we introduced the term multiplication.

Like, 5 + 5 + 5 + 5 = 4 × 5 = 20

In the same way, if we have to multiply the same number, again and again, we introduce the term exponent.

Ex, 2 × 2 × 2 × 2 × 2 = 25

So, in this article, we will discuss the exponent and powers and how it’s different rule is used in problem-solving.

Exponent is defined as the number of times a number is multiplied by itself.

Suppose, 5 is multiplied 4 times.

5 × 5 × 5 × 5 = 54

Here, the number which is multiplied is called as base i.e. 5, and the number of times it multiplied is called as power or index or exponent, i.e. 4.

We will read it as ‘five raised to the power four’ or ‘five to the power four’ or ‘fourth power of five’.

54 is called as exponential form or exponential notation of 625.

### Rules of Exponents

Rule 1: When the number is multiplied with different power but the same base then their power is added.

am × an = a(m+n)

Example, 23 × 22 = 2(3+2) = 25

Rule 2: When the number is multiplied with a different base but the same power then their base is multiplied.

aⁿ × bⁿ = (ab)ⁿ

Example : 2³ × 3³ = (2 × 3 )³ = 6³

Rule 3: When a number has the power of its power then the power gets multiplied.

(am)n = a(m×n)

Example: (2³)4 = 2(3×4) = 212

Rule 4: When the number is divided with different power but the same base then their denominator’s power is subtracted from the numerator’s power or divisor’s power is subtracted from dividend’s power.

am ÷ aⁿ = a(m-n)

Example: 26 ÷ 25 = 2(6-5)

Rule 5: When the number is divided with a different base but the same power then their base is divided and power remains the same.

am ÷ bm = (a ÷ b)m

Example: 3² ÷ 4² = (3×4)²

Rule 6: Negative power of a number represents the reciprocal of itself.

a(-n) = 1/an

Example: 5(-2) = 1/5²

Rule 7: Zero power of any number is equal to 1.

a0 = 1

Example: 230 = 1

Concept:

1. To solve the exponent problem, try to find out which of the above rule be applied.
2. Use the property and reduce the problem in the simplest form.
3. Do the proper calculation and get the final answer.

### Solve the expression: (7/3)(-3)

Solution:

We have to solve (7/3)(-3).

Base of the above problem is (7/3) and power is {-3}.

Negative power is introduced in rule number 6, i.e., a(-n) = 1/an

Negative power of any number change the base into its reciprocal.

Reciprocal of 7/3 = 3/7

Since their power will remain same,

(7/3)(-3) = (3/7)3

Now expand (3/7)3 using reverse of rule number 5.

= (33)/(73)

= (3×3×3)/(7×7×7)

= 27/343

So, the final answer of (7/3)(-3) is 27/343.

### Similar Questions

Question 1: Solve (2/3)(-2). What rule does this follow?

Solution:

We have to solve (2/3)(-2).

Base of the above problem is (2/3) and power is {-2}.

Negative power is introduced in rule number 6, i.e., a(-n) = 1/an

Negative power of any number change the base into its reciprocal.

Reciprocal of 2/3 = 3/2

Since their power will remain same,

(2/3)(-2) = (3/2)2

Now expand (3/2)2 using reverse of rule number 5.

= (32)/(22)

= (3×3)/(2×2)

= 9/4

So, the final answer of  (2/3)(-2) is 9/4.

Question 2: Solve (1/3)(-3). What rule does this follow?

Solution:

We have to solve (1/3)(-3).

Base of the above problem is (1/3) and power is {-3}.

Negative power is introduced in rule number 6, i.e., a(-n) = 1/an

Negative power of any number change the base into its reciprocal.

So, the reciprocal of 1/3 is 3.

Since their power will remain same,

(1/3)(-3) = (3)3

Now expand (3)3.

= 3 × 3 × 3

= 27

So, the final answer of (1/3)(-3) is 27.

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