Question

How do you simplify $\dfrac{{6{f^{ - 2}}{g^3}{h^5}}}{{54{f^{ - 2}}{g^{ - 5}}{h^3}}}$?

Answer 1

Hint: Here, we will use the law of negative power rule and will apply to the given expression and then will simplify for the resultant required value.

Complete step by step answer:
Take the given expression: $\dfrac{{6{f^{ - 2}}{g^3}{h^5}}}{{54{f^{ - 2}}{g^{ - 5}}{h^3}}}$
Above expression can be re-written as - $ = \dfrac{{6{f^{ - 2}}{g^3}{h^5}}}{{6 \times 9{f^{ - 2}}{g^{ - 5}}{h^3}}}$
Common factors from the numerator and the denominator cancels each other. Therefore remove from the numerator and the denominator.
$ = \dfrac{{{f^{ - 2}}{g^3}{h^5}}}{{9{f^{ - 2}}{g^{ - 5}}{h^3}}}$
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.
$ = \dfrac{{{f^{ - 2 + 2}}{g^{3 + 5}}{h^{5 - 3}}}}{9}$
Simplify the above expression –
$ = \dfrac{{{f^0}{g^8}{h^2}}}{9}$
Any number with the power zero is always one.
$ = \dfrac{{{g^8}{h^2}}}{9}$
This is the required solution

Additional Information:
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.

Note: Don’t be confused between power of a power rule and the power of the product rule.
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.