Question

Write the laws of exponents and also make some examples of these

Answer 1

Answer:

Law of Reciprocal: $a^{-n} =\frac{1}{a^{n} }$

Exponent with Fractional Index: $x^{\frac{m}{n} } =\sqrt[n]{x^{m} }$

Product Law of Exponents: $x^{m}\times x^{n}=x^{m+n}$

Power of Product Rule: $(a\times b)^{n} = a^{n} \times b^{n}$

Quotient Law of Exponents: $x^{m} \div x^{n}=x^{m-n}$

Power Law of Exponents: $(x^{m}) ^{n} =x^{mn}$

Power of Quotient Rule: $(\frac{a}{b})^{n} = \frac{a^{n} }{b^{n}}$

Step-by-step explanation:

Law of Reciprocal: $a^{-n} =\frac{1}{a^{n} }$

Example:

$a^{-5} =\frac{1}{a^{5} }$

Exponent with Fractional Index: $x^{\frac{m}{n} } =\sqrt[n]{x^{m} }$

Example:

$x^{\frac{5}{2} } =\sqrt[2]{x^{5} }$

Product Law of Exponents: $x^{m}\times x^{n}=x^{m+n}$

Example:

$x^{2}\times x^{5}=x^{2+5}\\x^{2}\times x^{5}=x^{7}$

Power of Product Rule: $(a\times b)^{n} = a^{n} \times b^{n}$

Example:

$(2\times 2)^{2} = 2^{2} \times 2^{2}\\(2\times 2)^{2} = 4 \times 4\\(2\times 2)^{2} = 16$

Quotient Law of Exponents: $x^{m} \div x^{n}=x^{m-n}$

Example:

$x^{5} \div x^{2}=x^{5-2}\\x^{5} \div x^{2}=x^{3}$

Power Law of Exponents: $(x^{m}) ^{n} =x^{mn}$

Example:

$(x^{2}) ^{5} =x^{2\times 5}\\(x^{2}) ^{5} =x^{10}$

Power of Quotient Rule: $(\frac{a}{b})^{n} = \frac{a^{n} }{b^{n}}$

Example:

$(\frac{5}{2})^{2} = \frac{5^{2} }{2^{2}}\\(\frac{5}{2})^{2} = \frac{25}{4}$