Question

Negative Exponents and Scientific Notation!
\(\Huge\mathbb{\color{coral}{Tutorial~For~Beginners!\}})\

Answer 1

If n is a positive integer and \[x \neq o\], then \[x ^{-n}\] Is defined as follows.:

Definition of a Negative Exponent \[x ^{-n}=\frac{ 1 }{ x ^{n} }\]

Answer 2

To evaluate a numerical expression with a negative exponent, first write the expression with a positive exponent. Then simplify.\[Evaluate~~~(a)~~2^{-5}~~~~~(b)~~3^{-4}\]\[(a)~~2^{-5}=~\frac{ 1 }{ 2^{5}}=\frac{ 1 }{ 32 }\]\[(b)~3^{-4}=\frac{ 1 }{ 3^{4}}=\frac{ 1 }{ 81 }\]

Answer 3

Laws of Exponents
The product rule\[x ^{a}*x ^{b}=x ^{a+b}\]The Quotient Rule \[\frac{ x ^{a} }{ x ^{b} }=x ^{a-b}~~ If~~a >b,~\frac{ x ^{a} }{ x ^{b}}=\frac{ 1 }{ x ^{b-a~} }~~If~~a <b\] Raising a power to a power\[(xy)^{a}=x ^{a}y ^{a},~~~~~(x ^{a})^{b}=x ^{ab},~~~~\left(\begin{matrix}x \\ y\end{matrix}\right)^{a}=\frac{ x ^{a} }{ y ^{a} }\]

Answer 4

By using the definition of a negative exponent and the properties of fraction, we can derive two more helpful proprieties of exponents.

Answer 5

Proprieties of Negative Exponents
\[\frac{ 1 }{ x ^{-n}}=x ^{n}~~~~~~~~~\frac{ x ^{-m} }{ y ^{-n}}=\frac{ y ^{n} }{ x ^{m}}\]

Answer 6

Simplify, write the expression so that no negative exponents appear.\[(a)~\frac{ 1 }{ x ^{-6} }\]\[(a) \frac{ 1 }{ x ^{-6} }=x ^{6}\][\[(b)~~~\frac{ x ^{-3}y ^{-2} }{ z ^{-4} }=\frac{ z ^{4} }{ x ^{3}y ^{2} }\]

Answer 7

Have to leave, will finish later!

Answer 8

kk XD