Question

Simplify $({2^5} \div {2^8}) \times {2^{ - 7}}$

Answer 1

Hint: In mathematical expression, the power is used to express the long expression in the short form which is used generally that represents the repeated multiplication of the same factor. Here we will use the multiplicative and division exponent rule to simplify the given expression for the resultant required value.

Complete step-by-step answer:
Take the given expression: $({2^5} \div {2^8}) \times {2^{ - 7}}$
The above expression can be re-written in the form of the fraction since division is given.
$ = \left( {\dfrac{{{2^5}}}{{{2^8}}}} \right) \times {2^{ - 7}}$
By using the law of the negative exponent rule which states that when the power and exponent moved to the denominator negative power becomes positive that is ${a^{ - n}} = \dfrac{1}{{{a^n}}}$
$ = {2^{5 - 8}} \times {2^{ - 7}}$
Simplify the above expression finding the difference of the powers –
$ = {2^{ - 3}} \times {2^{ - 7}}$
When bases are the same, powers are added when there is a multiplication sign in between.
$ = {2^{ - 10}}$
Hence, the required solution is $({2^5} \div {2^8}) \times {2^{ - 7}} = {2^{ - 10}}$

Note: Do not get confused between the positive and the negative power and exponents and apply accordingly. When the expression is in the denominator then powers of the sign are changed when moved to the numerator. Positive term changes to the negative term and vice-versa.