The blank is -8
Step-by-step explanation:
Let us revise some rules of indices:
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{5}[/tex] × [tex]4^{x}[/tex]
∵ All bases are equal
∴ Use the first and third rule above to find x
∵ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{3+-6}[/tex]
∴ [tex]4^{3}[/tex] × [tex]4^{-6}[/tex] = [tex]4^{-3}[/tex] ⇒ L.H.S
∵ [tex]4^{5}[/tex] × [tex]4^{x}[/tex] = [tex]4^{5+x}[/tex] ⇒ R.H.S
Equate L.H.S and R.H.S
∴ [tex]4^{-3}[/tex] = [tex]4^{5+x}[/tex]
Equate the indices of the two sides
∴ -3 = 5 + x
- Subtract 5 from both sides
∴ -8 = x
∵ x represents the blank
∴ The blank = -8
The blank is -8
Learn more:
You can learn more about the indices in brainly.com/question/4419221
#LearnwithBrainly
