Question

If $(9 {}^{n} \times 3 {}^{2} (3 {}^{ \frac{ - n}{2} } ) {}^{ - 2} - 27 {}^{n} ) \div 3 {}^{3m} \times 2 {}^{3} = \frac{1}{27}$
then prove that m – n = 1​

Answer 1

Answer:

See the above attachment.

Explanation:

You can solve it easily if you remember Rules of exponent or laws of exponent.

Rules of exponent:

1) Multiplication rule ➝

$a {}^{x} \times a {}^{y} = a {}^{x + y}$

2) Division rule ➝

$a {}^{x} \div a {}^{y} = a {}^{x - y}$

3) Power of a power rule ➝

$(a {}^{x} ) {}^{y} = a {}^{xy}$

4) Power of a product rule ➝

$(ab) {}^{x} = a {}^{x} b {}^{x}$

5) Power of a fraction rule ➝

$( \frac{a}{b} ) {}^{x} = \frac{a {}^{x} }{b {}^{x} }$

6) Zero exponent ➝

$a {}^{0} = 1$

7) Negative exponent ➝

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

8) Fractional exponent ➝

$a \frac{x}{y} = \sqrt[y]{ {a}^{x} }$