Question

Which expressions are equivalent to 4^3 x 4^-5?

Choose all answers that are correct.

A)
4^-2

B)
1/16

C)
4^-15

D)
0.0625

E)
16^-1

F)
1/4^15

G)
16^-2

H)
1/4^2

I)
(4^-1)^2

J)
4^3/4^5

Answer 1

`\large\begin{array}{l}\mathsf{(1)/(16)=0.0625~~~~\checkmark}\end{array}`


The definitions:



`\large\begin{array}{l}\fbox{$\mathsf{a^a\cdot a^b=a^(a+b)$ }}\\\\\\\mathsf{~So...}\\\\\\\mathsf{~4^3\cdot 4^(-5)\Leftrightarrow4^(3+(-5))\Leftrightarrow4^(3-5)\Leftrightarrow~4^(-2)\Leftrightarrow(1)/(4^2)\Leftrightarrow(1)/(16)}~~~~\checkmark\end`



`\large\begin{array}{l}\fbox{$\mathsf{a^(-b)=(1)/(a^b)}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{4^(-2)~\Leftrightarrow~(1)/(4^2) }~\Leftrightarrow~(1)/(16)~~~~\checkmark\end{array}`



`\large\begin{array}{l}\fbox{$\mathsf{a^(-1)=(1)/(a)}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{16^(-1)=(1)/(16)}~~~~\checkmark\end{array}`



`\large\begin{array}{l}\fbox{$\mathsf{\begin{pmatrix}(a)/(b)\end{pmatrix}^2= (a^2)/(b^2)}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{\begin{pmatrix} (1)/(4) \end{pmatrix}^2~\Leftrightarrow~(1^2)/(4^2)~\Leftrightarrow~ (1)/(16)}~~~~\checkmark\end{array}`



`\large\begin{array}{l}\fbox{$\mathsf{(a^b)^c=a^(b\cdot c)}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{(4^(-1))^2~\Leftrightarrow~4^((-1)\cdot 2)~\Leftrightarrow~4^(-2)~\Leftrightarrow~(1)/(4^2)~\Leftrightarrow~ (1)/(16)~~~~\checkmark}\end{array}`



`\large\begin{array}{l}\fbox{$\mathsf{(a^b)/(a^c)=a^(b-c)}$}\\\\\\\mathsf{So...}\\\\\\\mathsf{(4^3)/(4^5)~\Leftrightarrow~4^(3-5)~\Leftrightarrow~4^(-2)~\Leftrightarrow~(1)/(4^2)~\Leftrightarrow~ (1)/(16) ~~~~\checkmark}\end{array}`



`\large\textsf{Choose all answers that are correct:}\\\\\mathsf{A)~~\checkmark}\\\mathsf{B)~~\checkmark}\\\mathsf{D)~~\checkmark}\\\mathsf{E)~~\checkmark}\\\mathsf{H)~~\checkmark}\\\mathsf{I)~~\checkmark}\\\mathsf{J)~~\checkmark}`