Exponents and powers: Class 7 maths video

0:00 Class 7 maths. Exponents and powers.

0:04 Welcome back to the superhero math academy!

0:07 I am Captain Calc, and today we unleash the super-powers of exponents to handle huge numbers with ease.

0:15 Introduction to Base and Exponent.

0:18 When a number is multiplied by itself repeatedly, we use exponents for short.

0:23 In 2⁴, 2 is called the base and 4 is called the exponent or index or power.

0:30 Try this one. Write 5 × 5 × 5 in exponential form.

0:36 Identify the repeating factor: 5.

0:40 Count how many times it repeats: 3 times.

0:43 Write base as 5 and exponent as 3.

0:47 So the answer is 5³.

0:50 Multiplying and Dividing Powers with the Same Base.

0:54 When multiplying powers with the same base, add their exponents: aᵐ × aⁿ = aᵐ⁺ⁿ.

1:04 When dividing powers with the same base, subtract their exponents: aᵐ ÷ aⁿ = aᵐ⁻ⁿ.

1:16 Try this one. Simplify 3⁴ × 3².

1:22 Check that bases are equal: both are 3.

1:26 Add the exponents: 4 + 2 = 6.

1:29 Write the answer in exponential form.

1:32 So the answer is 3⁶.

1:35 Power of a Power and Zero Exponent.

1:38 To raise a power to another power, multiply the exponents: (aᵐ)ⁿ = aᵐⁿ.

1:48 Any non-zero number raised to the power 0 equals 1: a⁰ = 1.

1:54 Try this one. Simplify (2³)².

1:59 Identify the inner exponent 3 and outer exponent 2.

2:04 Multiply exponents: 3 × 2 = 6.

2:08 Write as 2⁶.

2:10 So the answer is 2⁶.

2:12 Expressing Large Numbers in Standard Form.

2:16 Any number can be written in standard form as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

2:26 Standard form makes reading and comparing giant numbers very easy.

2:31 Try this one. Express 45000 in standard form.

2:37 Place the decimal after the first non-zero digit: 4.5.

2:42 Count shift places from original end to new position: 4 places.

2:47 Write as 4.5 × 10⁴.

2:50 So the answer is 4.5 × 10⁴.

2:54 Your turn. Express 64 as a power of base 2. Pause the video, and try it.

3:03 The answer is 2⁶.

3:05 Well done! Now try the practice and the quiz in this lesson on LearnFun.