# Base and exponent pdf with answers 7th t1s1

In mathematics, the concept of exponents is a essential device that allows simplify repeated multiplication of the equal range. This article will manual you via the fundamentals of base and exponent, provide examples, and offer sporting events with solutions that will help you draw close the concept.

## What are Base and Exponent?

An exponent tells us how in many instances to multiply more than a few by using itself. The quantity being increased is called the **base**, and the exponent is the small wide variety written above and to the proper of the bottom.

For example, in 232^323:

- 2 is the base.
- three is the exponent.

This approach 232^323 is the same as 2×2×22 instances 2 times 22×2×2, which equals eight.

## Notation and Terminology

**Base**: The wide variety this is being extended.**Exponent**: The range that tells how**often the bottom**is increased with the aid of itself.**Power**: The end result of the bottom raised to the exponent.

## Examples and Explanation

**525^252**

**Base**: 5**Exponent**: 2**Calculation**: five×5=255 times 5 = 255×5=25**Power**: 25

**343^434**

**Base**: three**Exponent**: 4**Calculation**: 3×three×three×3=813 times three times 3 instances three = 813×three×three×3=81**Power**: 81

**10310^3103**

**Base**: 10**Exponent**: three**Calculation**: 10×10×10=100010 times 10 instances 10 = 100010×10×10=1000**Power**: 1000

## Rules of Exponents

**Multiplying with the same base**:

- am×an=am+na^m times a^n = a^m+nam×an=am+n
- Example: 23×24=23+4=27=1282^3 times 2^four = 2^3+four = 2^7 = 12823×24=23+4=27=128

**Dividing with the identical base**:

- am÷an=am−na^m div a^n = a^m-nam÷an=am−n
- Example: 54÷52=54−2=52=255^4 div five^2 = five^4-2 = 5^2 = 2554÷52=54−2=52=25

**Power of a energy**:

- (am)n=am×n(a^m)^n = a^m instances n(am)n=am×n
- Example: (32)three=32×3=36=729(3^2)^three = 3^2 times 3 = 3^6 = 729(32)3=32×3=36=729

**Power of a product**:

- (ab)n=an×bn(ab)^n = a^n times b^n(ab)n=an×bn
- Example: (2×three)2=22×32=four×nine=36(2 instances three)^2 = 2^2 times 3^2 = four times nine = 36(2×3)2=22×32=4×9=36

**Zero exponent**:

- a0=1a^zero = 1a0=1 (where a≠0a neq 0a=zero)
- Example: 70=17^0 = one hundred seventy=1

## Practice Problems with Answers

**Calculate 434^343**:

- Solution: 4×four×4=644 times 4 instances four = 644×4×four=64

**Simplify 25×222^five instances 2^225×22**:

- Solution: 25+2=27=1282^5+2 = 2^7 = 12825+2=27=128

**Evaluate (fifty two)three(five^2)^three(fifty two)three**:

- Solution: fifty two×three=56=156255^2 instances three = five^6 = 1562552×3=56=15625

**Find the fee of 104÷10210^four div 10^2104÷102**:

- Solution: 104−2=102=10010^four-2 = 10^2 = 100104−2=102=one hundred

**Calculate (3×four)2(three instances 4)^2(three×4)2**:

- Solution: 32×forty two=nine×16=1443^2 instances four^2 = 9 times sixteen = 14432×42=nine×sixteen=one hundred forty four

## Summary

Understanding the standards of base and exponent is vital for simplifying and fixing mathematical troubles involving repeated multiplication. By studying the regulations of exponents, students can manage lots of expressions and equations more effectively.

## Additional Exercises

- Simplify sixty two×636^2 instances 6^362×63.
- Evaluate ninety three÷99^three div 993÷9.
- Calculate (23)2(2^3)^2(23)2.
- Find the value of (four×5)2(four times five)^2(four×5)2.
- Simplify 808^080.

## Answers to Additional Exercises

- 62+three=65=77766^2+three = 6^five = 777662+3=65=7776
- ninety three−1=ninety two=819^3-1 = 9^2 = 8193−1=ninety two=eighty one
- 23×2=26=642^three times 2 = 2^6 = 6423×2=26=64
- 42×52=sixteen×25=4004^2 times 5^2 = sixteen times 25 = 40042×fifty two=16×25=four hundred
- 80=18^0 = one hundred eighty=1

By practising those issues and understanding the policies of exponents, you becomes extra comfortable with those concepts and geared up to tackle more complex mathematical demanding situations.