Question

Four to the power of three times four to the power of negative six is equal to four to the power of five times four to the power of blank

Answer 1

The blank is -8

Step-by-step explanation:

Let us revise some rules of indices:

• $a^{m}$ × $a^{n}$ = $a^{m+n}$
• $a^{m}$ ÷  $a^{n}$ = $a^{m-n}$
• $a^{m}$ =  $a^{n}$ , them m = n

∵ $4^{3}$ × $4^{-6}$ = $4^{5}$ × $4^{x}$

∵ All bases are equal

∴ Use the first and third rule above to find x

∵  $4^{3}$ × $4^{-6}$ = $4^{3+-6}$

∴  $4^{3}$ × $4^{-6}$ = $4^{-3}$ ⇒ L.H.S

∵  $4^{5}$ × $4^{x}$ = $4^{5+x}$ ⇒ R.H.S

Equate L.H.S and R.H.S

∴  $4^{-3}$ =  $4^{5+x}$

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

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