Exponents and powers are a method to express repeated multiplication of the same number. For eg- 7×7×7 can be written as 73 where 7 is the base and 3 is the exponent. It is most commonly used to express the powers of 10 to write a very large number in a convenient manner. For eg- 1000 can be written as 103.
Laws of Exponents
- To multiply two exponential numbers with the same bases, the exponents are added and the base remains the same.
For eg- am × an = am+n. - When the exponent has another exponent, the base remains the same but the powers are multiplied.
For eg- (am)n = am×n. - To divide two exponential numbers with the same bases, the exponents are subtracted and the base remains the same.
For eg- am/an = am-n.
What is a Power Notation?
Power notation is a method to express numbers that are very large or very small. For eg- 1000000000000 can be written as 1012 and 0.00000026 can be written as 2.6 × 10-7.
Steps to calculate the value of an exponential number:
- Write the number with its exponent.
- Multiply the number with itself for the number of times equal to its power.
- Make sure the calculation is correct.
What is 6th to the 3rd power?
Solution:
Given that the number is 6 and the power is 3.
Write the number with its exponent.
63 = 6 × 6 × 6
63 = 216
Hence, the value of 6 to the 3rd power is 216.
Similar Questions
Question 1: What is the 12th to the 4th power?
Solution:
Given that the number is 12 and the power is 4.
Write the number with its exponent.
124 = 12 × 12 × 12 × 12
124 = 20736
Hence, the value of 12 to the 4th power is 20736.
Question 2: What is the 3rd to the 6th power?
Solution:
Given that the number is 3 and the power is 6.
Write the number with its exponent.
36 = 3 × 3 × 3 × 3 × 3 × 3
36 = 729
Hence, the value of 3 to the 6th power is 729.
Question 3: What is the 15th to the 3rd power?
Solution:
Given that the number is 15 and the power is 3.
Write the number with its exponent.
153 = 15 × 15 × 15
153 = 3375
Hence, the value of 15 to the 3rd power is 3375.