Question

which expression is equivalent to 5^-3 x 5^7/5^-7

A 5^-42
B 25^-42
C 25^11
D 5^11

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the given expression, we can use the rule of exponents that states: 𝑎^(𝑚) / 𝑎^(𝑛) = 𝑎^(𝑚−𝑛).

Using this rule, we can rewrite the expression as:
5^(-3 + 7) / 5^(-7) = 5^4 / 5^(-7)

Using another rule of exponents, 𝑎^𝑚 / 𝑎^n = 𝑎^(𝑚−𝑛), we can subtract the exponents:
5^4 / 5^(-7) = 5^(4-(-7)) = 5^(4+7) = 5^11

Therefore, the expression is equivalent to 5^11.

The correct answer is D) 5^11.

Answer 2

its b

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in the previous response.

To simplify the given expression, we can use the rule of exponents that states: 𝑎^𝑚 × 𝑎^𝑛 = 𝑎^(𝑚+𝑛).

Using this rule, we can rewrite the expression as:
5^-3 × 5^7 / 5^-7 = 5^(7 - 3) / 5^-7 = 5^4 / 5^-7

Using another rule of exponents, 𝑎^𝑚 / 𝑎^n = 𝑎^(𝑚−𝑛), we can subtract the exponents:
5^4 / 5^-7 = 5^(4 - (-7)) = 5^(4 + 7) = 5^11

Therefore, the expression is equivalent to 5^11.

The correct answer is D) 5^11.