Exponents (Including Laws of Exponents)
ICSE Class 7 · Mathematics · Chapter 5
What this chapter covers
- Repeated multiplication and exponential form
- Writing numbers as powers
- Comparing powers
- Laws of exponents: the product law
- Laws of exponents: the quotient law
- Laws of exponents: the power law
- The zero exponent
- Using the laws together
- Exponents in daily life
Key points
- Repeated multiplication of the same number is written in exponential form, such as 3 × 3 × 3 × 3 = 34.
- In an, a is the base and n is the exponent; the exponent counts how many times the base is a factor.
- A number to the power 2 is its square, and to the power 3 is its cube; any number to the power 1 is itself.
- 1 raised to any power is 1, and 10n is 1 followed by n zeros.
- Every natural number greater than 1 can be written as a product of powers of primes, such as 360 = 23 × 32 × 5.
- To compare powers, find their values or write them with the same base.
- Product law: am × an = am+n.
- Quotient law: am ÷ an = am-n, for a not zero and m > n.
- Power law: (am)n = amn.
- Zero exponent: a0 = 1 for any a that is not zero.
- The laws work only for powers with the same base; with different bases, work with each base separately.
- Doubling, tripling and multiplying by ten again and again in daily life are all described by exponents.
Questions answered
In 95, name the base and the exponent, and write the power in expanded form.
The base is 9 and the exponent is 5. The expanded form is 9 × 9 × 9 × 9 × 9.
Find the value of 44 and of 31.
44 = 4 × 4 × 4 × 4 = 256, and 31 = 3.
Express 3375 as a product of powers of primes.
3375 = 3 × 3 × 3 × 5 × 5 × 5 = 33 × 53.
Which is greater, 28 or 82? Give a reason.
28 = 256 and 82 = 64, so 28 is greater.
Simplify 114 × 116 and name the law you used.
1110, by the product law (keep the base, add the exponents).
Simplify (69)/(66) and find its value.
69-6 = 63 = 216, by the quotient law.
Simplify (73)4.
73 × 4 = 712, by the power law.
Find the value of 150 + 23.
150 = 1 and 23 = 8, so the value is 1 + 8 = 9.