Question

How do you simplify ${\left( {\dfrac{3}{5}} \right)^{ - 2}}$?

Answer 1

Hint: The power is used to express mathematical equations in the short form; it is an expression that represents the repeated multiplication of the same factor. For example - $2 \times 2 \times 2$ can be expressed as ${2^3}$. Here, the number two is called the base and the exponent represents the number of times the base is used as the factor. Here we will apply the power and negative exponent rule and simplify the given expression with the squares of the given term.

Complete step-by-step solution:
Take the given expression: ${\left( {\dfrac{3}{5}} \right)^{ - 2}}$
By the negative exponent rule- the negative exponents in the numerator when moved to the denominator become positive and vice-versa. Such as ${a^{ - n}} = \dfrac{1}{{{a^n}}}$
Here in other words, the negative power of the denominator when moved to the numerator becomes positive and the positive power becomes negative.
$= {\left( {\dfrac{5}{3}} \right)^2}$
$= {\left( {\dfrac{5\times 5 }{3\times 3 }} \right)^2}$
Simplify the above expression –
$= \left( {\dfrac{{25}}{9}} \right)$
This is the required solution.

Thus the required solution is $ \left( {\dfrac{{25}}{9}} \right)$.

Note: Remember the seven basic rules of the exponent or the laws of exponents to solve these types of questions. Make sure to go through the below mentioned rules, it describes how to solve different types of exponents problems and how to add, subtract, multiply and divide the exponents.
- Product of powers rule
- Quotient of powers rule
- Power of a power rule
- Power of a product rule
- Power of a quotient rule
- Zero power rule