Indices -same ground number

which of these are the next step(s) in simplifying the indices?

 $3\times3^{\left(n-1\right)}$  

•  $3^1\times3^{\left(n-1\right)}\ =\ 3^{\left(1+n-1\right)}=3^n$  

•  $3^{\left(0+n+1\right)}=3^{\left(n+1\right)}$  

•  $3^1\ \times3^n\times3^1=3^{\left(2n\right)}$  

Which statement is true?

• $x^4\times x^5=x^9$

• $x^4\times x^5=x^{20}$

• $x^4\times x^5=x^{\left(\frac{4}{5}\right)}$

True of false?

 $\left(\frac{1}{3}\right)^{\left(n-1\right)}=\left(\frac{1}{3}\right)^n\left(\frac{1}{3}\right)^{-1}$  

• true

• false

Which answer is correct?

 $\left(\frac{1}{5}\right)^{-1}=$  

•  $5$  
  

•  $-5$  
  

•  $-\frac{1}{5}$  

Choose correct answer:

 $\left(\frac{1}{3}\right)^{\left(n-1\right)}=$  

•  $3\left(\frac{1}{3}\right)^n$  

•  $\frac{1}{3}\left(\frac{1}{3}\right)^n$  

•  $-\frac{1}{3}\left(\frac{1}{3}\right)^n$  

 $25\left(5\right)^{\left(n-1\right)}=$  

•  $25\left(5\right)^n\left(5\right)^{-1}=25\left(5\right)^n\left(\frac{1}{5}\right)=5\left(5\right)^n$  

•  $25\left(5\right)^n\left(5\right)^{-1\ }=-5\times25\left(5\right)^n=-125\left(5\right)^n$  

•  $25\left(5\right)^{\left(n-1\right)}=5^2\left(5\right)^{\left(n-1\right)}=\left(5\right)^{\left(2n-2\right)}$  

 $\left(\frac{1}{4}\right)^{-1}=$  

•  $4$  

•  $-4$  

•  $-\frac{1}{4}$ 

 $\frac{1}{7}=$  

•  $7^{-1}$  

•  $-7^{-1}$  

•  $-\left(\frac{1}{7}\right)^{-1}$  

 $3^{\left(n-1\right)}=$  

•  $\frac{1}{3}\times3^n$  

•  $-\frac{1}{3}\times3^n$  

•  $3\times3^n$  

 $2\times4^{\left(n-1\right)\ }=$  

•  $2\times4^n\times4^{-1}=2\times4^n\times\frac{1}{4}=\frac{1}{2}\left(4\right)^n$  

•  $2\times4^n\times4^{-1}=2\times4^n\times\left(-4\right)=-8\left(4\right)^n$  

•  $2\times\left(-4\right)^n=-8^n$