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Which expression is equivalent to [tex]4^7*4^{-5}[/tex]? A. [tex]4^{12}[/tex] B. [tex]4^2[/tex] C. [tex]4^{-2}[/tex] D. [tex]4^{-35}[/tex]

Respuesta :

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Answer:

B. [tex]4^2[/tex]

Step-by-step explanation:

[tex]4^7 \times 4^{-5}[/tex]

Apply rule (if bases are same) : [tex]a^b \times a^c = a^{b + c}[/tex]

[tex]4^{7 + -5}[/tex]

Add exponents.

[tex]=4^2[/tex]

Answer:

[tex] {4}^{2} [/tex]

Step by step explanation

[tex] {4}^{7} \times {4}^{ - 5} [/tex]

Use product law of indices

i.e

[tex] {x}^{m} \times {x}^{n} = {x}^{m + n} [/tex]

( powers are added in multiplication of same base)

[tex] = {4}^{7 + ( - 5)} [/tex]

[tex] = {4}^{7 - 5} [/tex]

[tex] = {4}^{2} [/tex]

Hope this helps...

Best regards!

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