The simplified form of the expression [tex]{2^2} \times \dfrac{{{2^3}}}{{{2^4}}}[/tex] is [tex]\boxed2.[/tex]
Further Explanation:
The rules of exponents are as follows,
1. [tex]\boxed{\left( {{x^m}} \right) \times \left( {{x^n}} \right) = {x^{m + n}}}[/tex]
2. [tex]\boxed{\dfrac{{{x^m}}}{{{x^n}}} = {x^{m - n}}}[/tex]
3. [tex]\boxed{{{\left( {{x^a}} \right)}^b} = {x^{a \times b}}}[/tex]
4. [tex]\boxed{{x^{\dfrac{m}{n}}} = \sqrt[n]{{{x^m}}}}[/tex]
Given:
The expression is [tex]A = {2^2} \times \dfrac{{{2^3}}}{{{2^4}}}.[/tex]
Calculation:
The given expression is [tex]A = {2^2} \times \dfrac{{{2^3}}}{{{2^4}}}.[/tex]
Solve the given expression to obtain the simplified form.
[tex]\begin{aligned}A &= {2^2} \times \frac{{{2^3}}}{{{2^4}}}\\&= \frac{{{2^2} \times {2^3}}}{{{2^4}}}\\&= \frac{{{2^{2 + 3}}}}{{{2^4}}}\\&= \frac{{{2^5}}}{{{2^4}}}\\\end{aligned}[/tex]
Further solve the above expression to obtain the simplified form.
[tex]\begin{aligned}A&= \dfrac{{{2^5}}}{{{2^4}}}\\&= \dfrac{{{2^{5 - 4}}}}{1}\\&= \dfrac{{{2^1}}}{1}\\ &= 2\\\end{aligned}[/tex]
The simplified form of the expression [tex]{2^2} \times \dfrac{{{2^3}}}{{{2^4}}}[/tex] is [tex]\boxed2.[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponents and Powers
Keywords: Solution, factorized form, [tex]x^12y^18+1[/tex], exponents, power, equation, power rule, exponent rule.
