Given the following expression:
[tex]\frac{(16 \sqrt[]{x})^2 }{y^{-1}}[/tex]You need to remember the Rules of Exponents shown below:
- Negative Exponent Rule:
[tex]b^{-n}=\frac{1}{b^n}[/tex]Where "b" is the base and "n" is the exponent.
- Fractional Exponent Rule:
[tex]b^{\frac{m}{n}}=\sqrt[n]{b^m}[/tex]- Power of a Product Rule:
[tex](ab)^m=a^mb^m[/tex]In this case, knowing the rules shown above, you can simplify the expression as follows:
1. Apply the Power of a Product Rule in the numerator:
[tex]=\frac{(16)^2(\sqrt[]{x})^2}{y^{-1}}=\frac{256^{}(\sqrt[]{x})^2}{y^{-1}}[/tex]2. Apply the Fractional Exponent Rule to simplify the square root:
[tex]=\frac{256^{}(x^{\frac{2}{2}})^{}}{y^{-1}}=\frac{256^{}(x^1)^{}}{y^{-1}}=\frac{256^{}x^{}}{y^{-1}}[/tex]3. Finally, apply the Negative Exponent Rule:
[tex]=(256^{}x)(y^1)=256^{}xy[/tex]Therefore, the answers are:
- Expression simplified:
[tex]256^{}xy[/tex]- Rules of Exponents used to simplify it:
1. Power of a Product Rule:
[tex](ab)^m=a^mb^m[/tex]2. Fractional Exponent Rule:
[tex]b^{\frac{m}{n}}=\sqrt[n]{b^m}[/tex]3. Negative Exponent Rule:
[tex]b^{-n}=\frac{1}{b^n}[/tex]